uuid
stringlengths 36
36
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stringclasses 6
values | has_image
bool 2
classes | image
stringclasses 160
values | problem_statement
stringlengths 32
784
| golden_answer
stringlengths 7
1.13k
|
---|---|---|---|---|---|
2d64140b-ec41-43b2-aa47-a02a2b515f51 | integral_calc | false | null | Compute the integral:
$$
\int x^{-4} \cdot \left(3+x^2\right)^{\frac{ 1 }{ 2 }} \, dx
$$ | $\int x^{-4} \cdot \left(3+x^2\right)^{\frac{ 1 }{ 2 }} \, dx$ = $C-\frac{1}{9}\cdot\left(1+\frac{3}{x^2}\right)\cdot\sqrt{1+\frac{3}{x^2}}$ |
2d799998-115a-489b-a48b-57090954303e | differential_calc | false | null | Compute the limit:
$$
\lim_{x \to 5} \left( \frac{ 3 \cdot x }{ x-5 }-\frac{ 3 }{ \ln\left(\frac{ x }{ 5 }\right) } \right)
$$ | $\lim_{x \to 5} \left( \frac{ 3 \cdot x }{ x-5 }-\frac{ 3 }{ \ln\left(\frac{ x }{ 5 }\right) } \right)$ = $\frac{3}{2}$ |
2e1592e8-b882-4761-b04a-613d85f94fbd | precalculus_review | false | null | Find the domain of the function $f(x) = \frac{ 1 }{ \sqrt{ |x| - x } }$. | The final answer: $(-\infty,0)$ |
2e672f49-9aec-4635-895a-d3f19e391509 | differential_calc | true | 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 | Use the following graphs and the limit laws to evaluate the limit $\lim_{x \to -9}\left(x \cdot f(x) + 2 \cdot g(x)\right)$. | $\lim_{x \to -9}\left(x \cdot f(x) + 2 \cdot g(x)\right)$ = $-46$ |
2e6afcbe-7883-4e94-9b96-cfc96e2841fc | integral_calc | false | null | Solve the integral:
$$
\int 3 \cdot \cot(-7 \cdot x)^6 \, dx
$$ | $\int 3 \cdot \cot(-7 \cdot x)^6 \, dx$ = $C-\frac{3}{7}\cdot\left(\frac{1}{5}\cdot\left(\cot(7\cdot x)\right)^5+\cot(7\cdot x)-\frac{1}{3}\cdot\left(\cot(7\cdot x)\right)^3-\arctan\left(\cot(7\cdot x)\right)\right)$ |
2e8c12b1-bd78-4c9e-a3f0-0e5888d2e71e | multivariable_calculus | false | null | Evaluate the triple integral of the function $f(x,y,z) = z$ over the solid $B$ bounded by the half-sphere $x^2+y^2+z^2=16$ with $z \ge 0$ and below by the cone $2 \cdot z^2 = x^2+y^2$. | $\int\int\int_{B}{f(x,y,z) d V}$ = $\frac{128\cdot\pi}{3}$ |
2ec21ca8-41a5-4d45-82cf-4ea1a390ce7b | multivariable_calculus | false | null | Find a normal vector and a tangent vector for $2 \cdot x^3 - x^2 \cdot y^2 = 3 \cdot x - y - 7$ at point $P : (1,-2)$ | Normal vector: $\vec{N}=\vec{i}-\vec{j}$
Tangent vector: $\vec{T}=\vec{i}+\vec{j}$ |
2ec678c4-d3d1-479f-9dc7-3117fb7bb232 | differential_calc | true | 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 | Use the following graph and find: $\lim_{x \to 0^{+}}\left(f(x)\right)$ | $\lim_{x \to 0^{+}}\left(f(x)\right)$: $-4$ |
2f336dde-88d0-403c-9bb7-60cb816dc6d7 | differential_calc | false | null | $f(x) = \frac{ 1 }{ 4 } \cdot \sqrt{x} + \frac{ 1 }{ x }$, $x > 0$. Determine:
1. Intervals where $f$ is increasing
2. Intervals where $f$ is decreasing
3. Local minima of $f$
4. Local maxima of $f$
5. Intervals where $f$ is concave up
6. Intervals where $f$ is concave down
7. The inflection points of $f$ | 1. Intervals where $f$ is increasing: $(4,\infty)$
2. Intervals where $f$ is decreasing: $(0,4)$
3. Local minima of $f$: $4$
4. Local maxima of $f$: None
5. Intervals where $f$ is concave up: $\left(0,8\cdot\sqrt[3]{2}\right)$
6. Intervals where $f$ is concave down: $\left(8\cdot\sqrt[3]{2},\infty\right)$
7. The inflection points of $f$: $8\cdot\sqrt[3]{2}$ |
2f7471d9-02df-48a7-8044-e5409141de5a | multivariable_calculus | false | null | Find the average value of the function $f(x,y) = \arctan(x \cdot y)$ over the region $R = [0,1] \times [0,1]$. | $f_{ave}$ = $\frac{\pi-\ln(4)}{4}-\frac{\pi^2}{48}$ |
2f7ca7bd-b50a-4cf6-9870-cec83f04faa0 | differential_calc | false | null | Find the extrema of a function $y = \frac{ 2 \cdot x^4 }{ 4 } - \frac{ x^3 }{ 3 } - \frac{ 3 \cdot x^2 }{ 2 } + 2$. Then determine the largest and smallest value of the function when $-2 \le x \le 4$. | 1. Extrema points: $P\left(\frac{3}{2},\frac{1}{32}\right)$, $P\left(-1,\frac{4}{3}\right)$, $P(0,2)$
2. The largest value: $\frac{254}{3}$
3. The smallest value: $\frac{1}{32}$ |
2fa3efa3-1a87-4757-879d-66fa65c0cf62 | algebra | false | null | Write an expression for a rational function with the given characteristics:
1. vertical asymptotes $x=-3$ and $x=2$,
2. x-intercepts at $P(1,0)$ and $P(-4,0)$,
3. y-intercept at $P(0,5)$. | The rational function satisfying the given conditions is $f(x)=\frac{15\cdot(x-1)\cdot(x+4)}{2\cdot(x+3)\cdot(x-2)}$ |
2fe7cf5b-86d4-417a-a942-46e2194625eb | integral_calc | false | null | Solve the integral:
$$
\int \cot(x)^4 \, dx
$$ | $\int \cot(x)^4 \, dx$ = $C+\cot(x)-\frac{1}{3}\cdot\left(\cot(x)\right)^3-\arctan\left(\cot(x)\right)$ |
2ff5a6e4-6a0a-48e5-adfc-bdaf179a7fc9 | multivariable_calculus | false | null | Use the method of Lagrange multipliers to maximize $U(x,y) = 8 \cdot x^{\frac{ 4 }{ 5 }} \cdot y^{\frac{ 1 }{ 5 }}$ subject to the constraint $4 \cdot x + 2 \cdot y = 12$. | Answer: maximum $16.715$ at $P(2.4,1.2)$ |
309063a4-cd05-4d2e-a3ff-4f5937d4df66 | integral_calc | true | 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 | Let $A$ be the region bounded by the graph $x=(y+2)^2$, $y=x-4$, $y=2$, and the $y$-axis as shown in the figure above.
1. Write, but do not evaluate, an expression involving one or more integrals that gives the volume of the solid generated when $A$ is revolved about the $y$-axis.
2. Find the value of the volume of the solid using the integral expression found in part (a). | 1. $\int_{-2}^0\left(\pi\cdot\left((y+2)^2\right)^2\right)dy+\int_0^2\left(\pi\cdot(y+4)^2\right)dy$
2. $179.28$ units³ |
30b1fff3-c7e8-4443-8b21-ad150fba7da0 | algebra | false | null | Note that $1 \in (-3,7)$. Think of the solution of the inequality $|x-1|<\delta$, where $\delta$ (delta, a Greek letter) is a constant.
Find the greatest $\delta$ so that the solution is completely on the interval $(-3,7)$.
[Hint: How far you can go within $(-3,7)$, starting from $1$?] | The final answer: $4$ |
30b647a3-04b2-4224-8e1d-9a46f4fe6103 | integral_calc | false | null | Solve the integral:
$$
\int \left(\frac{ x+3 }{ x-3 }\right)^{\frac{ 3 }{ 2 }} \, dx
$$ | $\int \left(\frac{ x+3 }{ x-3 }\right)^{\frac{ 3 }{ 2 }} \, dx$ = $C+\sqrt{\frac{x+3}{x-3}}\cdot(x-15)-9\cdot\ln\left(\left|\frac{\sqrt{x-3}-\sqrt{x+3}}{\sqrt{x-3}+\sqrt{x+3}}\right|\right)$ |
30cec86e-4be2-4e33-b449-e66f79f364a2 | multivariable_calculus | false | null | $E$ is located above the xy-plane, below $z=1$, outside the one-sheeted hyperboloid $x^2+y^2-z^2=1$, and inside the cylinder $x^2+y^2=2$. Find the volume of $E$. | Volume = $\frac{2\cdot\pi}{3}$ |
30d63199-0a17-480a-9a4e-b3761098338b | algebra | true | 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 | Use the graph of the function to estimate the intervals on which the function is increasing or decreasing.
A function is increasing/decreasing on an interval when its values increase/decrease as $x$ values increase (moving to the right on the graph). | The final answer:
Interval(s) of increase: $(-1.5,2)$
Interval(s) of decrease: $(-\infty,-1.5)\cup(2,\infty)$ |
3105d97f-f772-43ee-ad96-a977b62b3322 | multivariable_calculus | false | null | Develop the Cartesian equation for the following parametric equations:
$x = 3 \cdot t + \frac{ 3 }{ 4 \cdot t }$
$y = 5 \cdot t - \frac{ 5 }{ 4 \cdot t }$ | The final answer: $\frac{x^2}{9}-\frac{y^2}{25}=1$ |
313f8edb-e1ee-4bc2-ac17-270dc7106f35 | multivariable_calculus | false | null | Evaluate the integral by choosing the order of integration:
$$
\int_{1}^e \int_{1}^e \left( \frac{ x \cdot \ln(y) }{ \sqrt{y} } + \frac{ y \cdot \ln(x) }{ \sqrt{x} } \right) \, dy \, dx
$$ | $\int_{1}^e \int_{1}^e \left( \frac{ x \cdot \ln(y) }{ \sqrt{y} } + \frac{ y \cdot \ln(x) }{ \sqrt{x} } \right) \, dy \, dx$ = $2\cdot\sqrt{e}+4\cdot e^2-4-2\cdot e^2\cdot\sqrt{e}$ |
31b62f10-54ed-4f45-a532-2220b453838d | differential_calc | false | null | Make full curve sketching of $y = \ln\left(\left|\frac{ 2 \cdot x-5 }{ 2 \cdot x+5 }\right|\right)$. Submit as your final answer:
1. The domain (in interval notation)
2. Vertical asymptotes
3. Horizontal asymptotes
4. Slant asymptotes
5. Intervals where the function is increasing
6. Intervals where the function is decreasing
7. Intervals where the function is concave up
8. Intervals where the function is concave down
9. Points of inflection | 1. The domain (in interval notation) $\left(-\infty,-\frac{5}{2}\right)\cup\left(-\frac{5}{2},\frac{5}{2}\right)\cup\left(\frac{5}{2},\infty\right)$
2. Vertical asymptotes $x=-\frac{5}{2}$, $x=\frac{5}{2}$
3. Horizontal asymptotes $y=0$
4. Slant asymptotes None
5. Intervals where the function is increasing $\left(-\infty,-\frac{5}{2}\right)$, $\left(-\frac{5}{2},0\right)$
6. Intervals where the function is decreasing $\left(-\frac{5}{2},\frac{5}{2}\right)$
7. Intervals where the function is concave up $\left(-\infty,-\frac{5}{2}\right)$, $\left(\frac{5}{2},\infty\right)$
8. Intervals where the function is concave down $\left(\frac{5}{2},\infty\right)$, $\left(0,\frac{5}{2}\right)$
9. Points of inflection $P(0,0)$ |
324f58d5-6dfb-461d-9750-6e713fedb6f6 | integral_calc | false | null | Compute the length of the arc $y = 3 \cdot \ln(2 \cdot x)$ between the points $x = \sqrt{7}$ and $x = 4$. | Arc Length: $1+\frac{3}{2}\cdot\ln\left(\frac{7}{4}\right)$ |
3265c2a2-779f-4ede-a31f-feb2dde5e7cf | sequences_series | false | null | Find $L=\lim_{n \to \infty}\left(x_{n}\right)$, where $x_{n} = \frac{ \sqrt{n^2+1} + \sqrt{n} }{ \sqrt[4]{n^3+n} - \sqrt{n} }$ is the general term of a sequence. | The final answer: $L=\infty$ |
32d27abf-2f33-48e4-84fb-756af840c821 | precalculus_review | false | null | Find points on a coordinate plane that satisfy the equation $x \cdot (x-2) + y \cdot (y+4) + 5 = 0$. | The final answer: $(1,-2)$ |
32f04626-b937-48c5-a7e7-708115124653 | precalculus_review | false | null | Find points on a coordinate plane that satisfy the equation $y = \sqrt{\ln\left(\cos(x)\right)}$. | The final answer: $(2\cdot k\cdot\pi,0)$ |
33478f29-8573-4922-a984-f7f20a3f68c9 | differential_calc | false | null | Compute the derivative $y^{(5)}$ of the function $y = e^{\frac{ x }{ 3 }} \cdot \sin\left(\frac{ x }{ 2 }\right)$. | $y^{(5)}$ = $\frac{1}{7776}\cdot e^{\frac{x}{3}}\cdot\left(122\cdot\sin\left(\frac{x}{2}\right)-597\cdot\cos\left(\frac{x}{2}\right)\right)$ |
3355c2b6-9095-4bb3-90ef-51b6fb9f3708 | algebra | false | null | Identify all points of removable discontinuity (singularity) of the function $f(x) = \frac{ x^2 - 4 }{ x - 2 }$. | $f(x)$ has removable discontinuities at $x=2$ |
337a55dc-e856-4e1e-b717-2c1ca37ca438 | differential_calc | false | null | The cost for printing a book can be given by the equation $C(x) = 1000 + 12 \cdot x + \frac{ 1 }{ 2 } \cdot x^{\frac{ 2 }{ 3 }}$. Use Newton’s method to find the break-even point if the printer sells each book for $\$20$. | $127$ books |
33d1cff7-b004-4c49-878f-f1056b5dd633 | multivariable_calculus | false | null | Use the method of Lagrange multipliers to find the maximum and minimum values of $f(x,y,z) = x^2 + y^2 + z^2$ subject to the constraint $x^4 + y^4 + z^4 = 1$. If there is no maximum or minimum, then write $\text{None}$ in the answer. | Maximum: $\sqrt{3}$
Minimum: $1$ |
34800a4c-8294-4b02-a23e-f4be6115f560 | differential_calc | true | 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 | Let $h$ be a function defined by $h(x) = \left(rac{ f(x) }{ g(x) }
ight)^2$.
Selected values of $f$ and $f'$ are shown in the table below.
The graph of $g$ is shown below.
If $f$ and $g$ are continuous functions, determine $h'(0)$ (else write None).
| $x$ | $f(x)$ | $f'(x)$ |
| --- | --- | --- |
| $0$ | $2$ | $5$ |
| $1$ | $1$ | $-2$ |
| $2$ | $4$ | $4$ |
| $3$ | $3$ | $-3$ | | $h'(0)$ = $\frac{4}{5}$ |
3497d594-978a-4c17-9210-5654e5e7023a | algebra | false | null | The unit price of an item affects its supply and demand. That is, if the unit price goes up, the demand for the item will usually decrease. For example, a local newspaper currently has $84\ 000$ subscribers at a quarterly charge of $\$30$. Market research has suggested that if the owners raise the price to $\$33$, they would lose $7000$ subscribers. Assuming that subscriptions are linearly related to the price, what price should the newspaper charge for a quarterly subscription to maximize their revenue? | The final answer: $33$ |
34bdbf1b-9f1b-43b3-9195-dabc016eb1a7 | differential_calc | false | null | Find the derivative of $f(x) = \frac{ \left(\left(\tan(x)\right)^2-1\right) \cdot \left(\left(\tan(x)\right)^4+10 \cdot \left(\tan(x)\right)^2+1\right) }{ 3 \cdot \left(\tan(x)\right)^3 }$ | The final answer: $f'(x)=\left(\tan(x)\right)^4+4\cdot\left(\tan(x)\right)^2+\frac{4}{\left(\tan(x)\right)^2}+\frac{1}{\left(\tan(x)\right)^4}+6$ |
34ee9891-810d-43a5-9a82-9d2c37ec5f6d | sequences_series | false | null | Decompose the function $f(x) = \frac{ 1 }{ 2 } \cdot (\pi-x)$ into a trigonometric series on the interval $[0,2 \cdot \pi]$. | The final answer: $f(x)=\sin(x)+\frac{1}{2}\cdot\sin(2\cdot x)+\frac{1}{3}\cdot\sin(3\cdot x)+\cdots+\frac{1}{n}\cdot\sin(n\cdot x)+\cdots$ |
34f480a3-bc95-4865-8a8a-cf0132878a01 | integral_calc | false | null | Compute the integral:
$$
\int_{0}^1 \frac{ \sqrt{x}+1 }{ \sqrt[3]{x}+1 } \, dx
$$ | $\int_{0}^1 \frac{ \sqrt{x}+1 }{ \sqrt[3]{x}+1 } \, dx$ = $3\cdot\ln(2)+\frac{3\cdot\pi}{2}-\frac{409}{70}$ |
35180e65-8d1d-4399-86d3-ca456db0e24c | multivariable_calculus | false | null | Evaluate the integral by choosing the order of integration:
$$
\int_{0}^1 \int_{0}^{\frac{ 1 }{ 2 }} \left(\arcsin(x) + \arcsin(y)\right) \, dy \, dx
$$ | $\int_{0}^1 \int_{0}^{\frac{ 1 }{ 2 }} \left(\arcsin(x) + \arcsin(y)\right) \, dy \, dx$ = $\frac{\pi}{12}+\frac{\sqrt{3}}{2}+\frac{\arcsin(1)}{2}-\frac{3}{2}$ |
35505dd4-7798-48a2-9d3b-11edc71de275 | multivariable_calculus | false | null | Compute the partial derivatives of the implicit function $z(x,y)$, given by the equation $-x-6 \cdot y+z=3 \cdot \cos(-x-6 \cdot y+z)$.
Submit as your final answer:
1. $\frac{\partial z}{\partial x}$;
2. $\frac{\partial z}{\partial y}$. | 1. $1$
2. $6$ |
3592c6d2-0fb1-4557-b219-d88f5b8a7401 | sequences_series | false | null | Find the Fourier integral of the function $q(x) = \begin{cases} 0, & x < 0 \\ \pi \cdot x, & 0 \le x \le 1 \\ 0, & x > 1 \end{cases}$ | $q(x) = $\int_0^\infty\left(\frac{\left(\alpha\cdot\sin\left(\alpha\right)+\cos\left(\alpha\right)-1\right)\cdot\cos\left(\alpha\cdot x\right)+\left(\sin\left(\alpha\right)-\alpha\cdot\cos\left(\alpha\right)\right)\cdot\sin\left(\alpha\cdot x\right)}{\alpha^2}\right)d\alpha$ |
35cb0f7d-db0d-494e-980b-55bd98f0170b | sequences_series | false | null | Find the Maclaurin series for the function: $f(x) = \cos(x) - x \cdot \sin(x)$. | The series: $\sum_{n=0}^\infty\left(\frac{(-1)^n\cdot(2\cdot n+1)\cdot x^{2\cdot n}}{(2\cdot n)!}\right)$ |
35e4725a-56f7-46f8-8115-a4f3b75a09a2 | integral_calc | true | 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 | The region bounded by the parabola $y^2 = 2 \cdot p \cdot x$ and the line AB is revolved about the Y-axis. The line AB passes through the focus of the parabola and is perpendicular to the X-axis. Find the volume of this solid of revolution using integration with respect to $y$. Use $p = \frac{ 1 }{ 2 }$. | Volume: $\frac{\pi}{20}$ |
363dd580-f1fc-4867-a6ef-db2a03139745 | differential_calc | false | null | Evaluate $\lim_{x \to 0^{+}}\left(\left(\frac{ \tan\left(\frac{ x }{ 2 }\right) }{ \frac{ x }{ 2 } }\right)^{\frac{ 3 }{ x^2 }}\right)$ using L'Hopital's Rule. | $\lim_{x \to 0^{+}}\left(\left(\frac{ \tan\left(\frac{ x }{ 2 }\right) }{ \frac{ x }{ 2 } }\right)^{\frac{ 3 }{ x^2 }}\right)$ = $e^{\frac{1}{4}}$ |
3655d579-c27c-463e-8ece-662e1f8a0b02 | algebra | false | null | A phone company has a monthly cellular plan, where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 410 minutes, the monthly cost will be $71.5. If the customer uses 720 minutes, the monthly cost will be $118.1.
1. Find a linear equation for the monthly cost of the cell plan as a function of $x$, the number of monthly minutes used.
2. Interpret the slope and y-intercept of the equation.
3. Use your equation to find the total monthly cost if 687 minutes are used. | 1. The monthly cost function is $C(x)=0.15\cdot x+10$
2. The flat monthly fee is $10$ and the fee for each additional minute used is $0.15$
3. The total monthly cost if 687 minutes are used is $113.05$ |
36585e1b-1b7a-4835-befc-4610d20674a1 | precalculus_review | false | null | A car is racing along a circular track with a diameter of 1 mile. A trainer standing in the center of the circle marks his progress every 5 seconds. After 5 seconds, the trainer has to turn $55^o$ to keep up with the car. How fast is the car traveling? | Velocity of car is $345.57519189$ mph. |
36e3fe5a-1d6e-4976-b51a-6eea157d5128 | precalculus_review | false | null | Find all values of $x$ that satisfy the following equation:
$$
\left|\left(x^2+4 \cdot x+9\right)+(2 \cdot x-3)\right|=\left|x^2+4 \cdot x+9\right|+|2 \cdot x-3|
$$ | The final answer: $x\ge\frac{3}{2}$ |
37440b24-a694-4066-acf5-e5dc13144552 | precalculus_review | false | null | Find the zeros of $\tan(x) + \tan\left(\frac{ \pi }{ 4 } + x\right) = -2$. | The final answer: $x_{1}=-\frac{ \pi }{ 3 }+\pi \cdot n$, $x_{2}=\frac{ \pi }{ 3 }+n \cdot \pi$ |
374da26c-e042-4624-9e44-edaf584b1909 | differential_calc | true | 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 | Analyze the graph of $f'$, then list all inflection points and intervals on which $f$ is concave up and concave down. | Inflection points at: $x=0$, $x=1$
Intervals where function is concave up: $(-\infty,0)$, $(1,\infty)$
Intervals where function is concave down: $(0,1)$ |
3761ac12-4b27-4ca2-8fd6-345ca0a137fe | precalculus_review | false | null | Calculate $E = \left(\sin\left(\frac{ \pi }{ 8 }\right)\right)^4 + \left(\sin\left(\frac{ 3 \cdot \pi }{ 8 }\right)\right)^4 + \left(\sin\left(\frac{ 5 \cdot \pi }{ 8 }\right)\right)^4 + \left(\sin\left(\frac{ 7 \cdot \pi }{ 8 }\right)\right)^4$ | The final answer: $E=\frac{3}{2}$ |
37d1acdf-64e4-4c6d-a76d-c273e763ad18 | multivariable_calculus | false | null | Compute the partial derivatives of the implicit function $z(x,y)$, given by the equation
$$
-10 \cdot x-9 \cdot y+8 \cdot z=4 \cdot \cos(-10 \cdot x-9 \cdot y+8 \cdot z)
$$
Submit as your final answer:
1. $\frac{\partial z}{\partial x}$;
2. $\frac{\partial z}{\partial y}$. | 1. $\frac{5}{4}$
2. $\frac{9}{8}$ |
37de6838-f6c9-47b8-8257-12db6a7f5b6b | multivariable_calculus | false | null | For the following exercise, line $L$ is given.
1. Find point $P$ that belongs to the line and direction vector $\vec{v}$ of the line. Express $\vec{v}$ in component form.
2. Find the distance from the origin to line $L$.
Line $L$: $-x = y + 1$, $z = 2$ | 1. $P$: $P(0,-1,2)$ ; $\vec{v}$= $\left\langle-1,1,0\right\rangle$
2. $d$= $\frac{3}{\sqrt{2}}$ |
37e7e328-accc-4a28-98f7-7391204c2892 | integral_calc | false | null | Compute the integral:
$$
\int x^{-6} \cdot \left(1+x^2\right)^{\frac{ 1 }{ 2 }} \, dx
$$ | $\int x^{-6} \cdot \left(1+x^2\right)^{\frac{ 1 }{ 2 }} \, dx$ = $C+\frac{1}{3}\cdot\left(\frac{1}{x^2}+1\right)\cdot\sqrt{\frac{1}{x^2}+1}-\frac{1}{5}\cdot\left(\frac{1}{x^2}+1\right)^2\cdot\sqrt{\frac{1}{x^2}+1}$ |
37f31f02-4302-49b8-bd61-4bad89d04fe7 | precalculus_review | false | null | Use the Rational Zero Theorem to find all real zeros of the following polynomial:
$p(x) = x^3 - 3 \cdot x^2 - 10 \cdot x + 24$ | The real zeros are $2$, $-3$, $4$ |
3868940c-d8fc-4b5f-a82d-15c0853f15b8 | sequences_series | false | null | Find the radius of convergence and the interval of convergence for the series:
$$
\sum_{n=0}^\infty \left(\frac{ x^n }{ n^n }\right)
$$ | $R$ = $\infty$
$I$ = $(-\infty,\infty)$ |
3882cc71-2ff8-4a16-8ebb-3eeee2365bfa | differential_calc | true | 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 | Use the following graphs and the limit laws to evaluate the limit $\lim_{x \to -5}\left(\frac{ 2+g(x) }{ f(x) }\right)$: | $\lim_{x \to -5}\left(\frac{ 2+g(x) }{ f(x) }\right)$ = $1$ |
38defb82-0872-4e28-80bc-d425575cf1ab | precalculus_review | false | null | Find the period of $f(x) = \left| \cos(x) \right|$ | The final answer: $T=\pi$ |
3934b610-d7c8-4cec-bef7-ed06c0b05391 | algebra | false | null | Rewrite the quadratic expression $x^2 - 11 \cdot x - 20$ by completing the square. | $x^2 - 11 \cdot x - 20$ = $(x-5.5)^2-50.25$ |
394e56e3-055c-4209-b8b1-1f2283907c2a | algebra | false | null | Use the fact that the vertex of the graph of the quadratic function is $(2,-3)$ and the graph opens up to find the domain and range of the function. | The domain is $(-\infty,\infty)$ and the range is $[-3,\infty)$ |
39955d74-b26d-4d7d-ae27-b93ee45f74dc | integral_calc | false | null | Compute the area of the figure bounded by curves $y = 2 \cdot x^2$, $y = 1 + x^2$, lines $x = 3$, $x = -2$, and the $x$-axis. | Area = $\frac{46}{3}$ |
39c876c6-191f-4992-b50f-f15595d08e4e | differential_calc | true | 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 | The following graph of the function $f$ satisfies $\lim_{x \to 3}f(x) = 2$. For $\varepsilon = 3$, find a value of $\delta > 0$ such that the precise definition of limit holds true. | $\delta \leq $1$$ |
3a761457-5727-4faa-b9c8-a9e3d0e1881e | precalculus_review | false | null | An alternating current for outlets in a home has voltage given by the function $V(t) = 150 \cdot \cos(368 \cdot t)$, where $V$ is the voltage in volts at time $t$ in seconds.
1. Find the period of the function.
2. Determine the number of periods that occur when $1$ sec. has passed. | 1. The period of the function is $\frac{\pi}{184}$
2. The number of periods that occur when $1$ sec. has passed is $58.56901906$ |
3a9ca0e5-d5e8-41d3-a45c-7623bbbb2969 | precalculus_review | false | null | Evaluate the definite integral. Express answer in exact form whenever possible:
$$
\int_{-\pi}^\pi \left(\cos(3 \cdot x)\right)^2 \, dx
$$ | $\int_{-\pi}^\pi \left(\cos(3 \cdot x)\right)^2 \, dx$ = $\pi$ |
3ae4b0b6-dcdf-4733-a2ff-2f6cccad2598 | integral_calc | false | null | Compute the integral:
$$
\int \frac{ -4 }{ 3+\sin(4 \cdot x)+\cos(4 \cdot x) } \, dx
$$ | $\int \frac{ -4 }{ 3+\sin(4 \cdot x)+\cos(4 \cdot x) } \, dx$ = $C-\frac{2}{\sqrt{7}}\cdot\arctan\left(\frac{2}{\sqrt{7}}\cdot\left(\frac{1}{2}+\tan(2\cdot x)\right)\right)$ |
3b116e5c-f065-4e95-8774-f422916f3e8a | differential_calc | false | null | Make full curve sketching of $y = \arcsin\left(\frac{ 1-x^2 }{ 1+x^2 }\right)$. Submit as your final answer:
1. The domain (in interval notation)
2. Vertical asymptotes
3. Horizontal asymptotes
4. Slant asymptotes
5. Intervals where the function is increasing
6. Intervals where the function is decreasing
7. Intervals where the function is concave up
8. Intervals where the function is concave down
9. Points of inflection | 1. The domain (in interval notation) $(-1\cdot\infty,\infty)$
2. Vertical asymptotes None
3. Horizontal asymptotes $y=-\frac{\pi}{2}$
4. Slant asymptotes None
5. Intervals where the function is increasing $(-\infty,0)$
6. Intervals where the function is decreasing $(0,\infty)$, $(-\infty,0)$
7. Intervals where the function is concave up $(0,\infty)$, $(-\infty,0)$
8. Intervals where the function is concave down None
9. Points of inflection None |
3b126d90-4cae-43c5-8f74-072d49ac068b | multivariable_calculus | false | null | Find the point on the surface $f(x,y) = x^2 + y^2 + 10$ nearest the plane $x + 2 \cdot y - z = 0$. Identify the point on the plane. | Answer: $P\left(\frac{47}{24},\frac{47}{12},\frac{235}{24}\right)$ |
3b3ba848-ee8f-4978-b0c2-ceb26a88779e | differential_calc | false | null | Sketch the curve:
$$
y = \frac{ x^3 }{ 4 \cdot (x+3)^2 }
$$
Provide the following:
1. The domain (in interval notation)
2. Vertical asymptotes
3. Horizontal asymptotes
4. Slant asymptotes
5. Intervals where the function is increasing
6. Intervals where the function is decreasing
7. Intervals where the function is concave up
8. Intervals where the function is concave down
9. Points of inflection | 1. The domain (in interval notation): $(-1\cdot\infty,-3)\cup(-3,\infty)$
2. Vertical asymptotes: $x=-3$
3. Horizontal asymptotes: None
4. Slant asymptotes: $y=\frac{x}{4}-\frac{3}{2}$
5. Intervals where the function is increasing: $(-\infty,-9)$, $(-3,0)$, $(0,\infty)$
6. Intervals where the function is decreasing: $(-9,-3)$
7. Intervals where the function is concave up: $(-\infty,-9)$, $(-3,0)$, $(0,\infty)$
8. Intervals where the function is concave down: $(-3,0)$, $(-\infty,-3)$
9. Points of inflection: $P(0,0)$ |
3b944c43-38f7-4bfb-a805-43620f329cf8 | integral_calc | true | 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 | The following table lists the electrical power in gigawatts—the rate at which energy is consumed—used in a certain city for different hours of the day, in a typical $24$-hour period, with hour $1$ corresponding to midnight to $1$ a.m.
Find the total amount of power in gigawatt-hours (gW-h) consumed by the city in a typical $24$-hour period. | $911$ gW-h. |
3ba2efcf-1203-4eaa-a8c6-c69f28313fa3 | precalculus_review | false | null | $P = \left(\frac{ 7 }{ 25 },y\right)$, $y>0$ is a point on the unit circle.
1. Find the (exact) missing coordinate value of the point.
2. Find the values of the six trigonometric functions for the angle $\theta$ with a terminal side that passes through point $P$.
Rationalize denominators. | 1. The (exact) missing coordinate value of the point is: $\frac{24}{25}$
2. The values of the six trigonometric functions are:
* $\sin\left(\theta\right)$ = $\frac{24}{25}$
* $\cos\left(\theta\right)$ = $\frac{7}{25}$
* $\tan\left(\theta\right)$ = $\frac{24}{7}$
* $\csc\left(\theta\right)$ = $\frac{25}{24}$
* $\sec\left(\theta\right)$ = $\frac{25}{7}$
* $\cot\left(\theta\right)$ = $\frac{7}{24}$ |
3bf5f05a-3a2f-4939-9cc2-52605b9db700 | integral_calc | false | null | Solve the integral:
$$
\int \sqrt{\frac{ -16 \cdot \sin(-10 \cdot x) }{ 25 \cdot \cos(-10 \cdot x)^9 }} \, dx
$$ | $\int \sqrt{\frac{ -16 \cdot \sin(-10 \cdot x) }{ 25 \cdot \cos(-10 \cdot x)^9 }} \, dx$ = $C+\frac{2}{25}\cdot\left(\frac{2}{3}\cdot\left(\tan(10\cdot x)\right)^{\frac{3}{2}}+\frac{2}{7}\cdot\left(\tan(10\cdot x)\right)^{\frac{7}{2}}\right)$ |
3c05e140-7754-4647-a453-9073ee403a29 | differential_calc | false | null | Find the derivative of $f(x) = \frac{ 1 }{ 15 } \cdot \left(\cos(x)\right)^3 \cdot \left(\left(\cos(x)\right)^2-5\right)$. | The final answer: $f'(x)=-\frac{\left(\cos(x)\right)^2}{15}\cdot\left(3\cdot\sin(x)\cdot\left(\left(\cos(x)\right)^2-5\right)+\cos(x)\cdot\sin(2\cdot x)\right)$ |
3c515761-f013-4a2c-b5f8-1a70be519118 | sequences_series | false | null | Compute $\sqrt[4]{90}$ with accuracy $0.0001$. | The final answer: $3.0801$ |
3c7f8f93-bdba-4b7d-8e4a-4908ee1082cd | algebra | false | null | Solve the following compound (double) inequality and write your final answer in interval notation:
$-4 < 3 \cdot x + 2 \le 18$ | The final answer: $\left(-2,\frac{16}{3}\right]$ |
3cc19800-9373-4d92-97b9-b6f37e135eba | differential_calc | true | 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 | Find the values of $a$ and $b$ that make continuous and differentiable at $x=1$. | The final answer:
$a = $-4$$
$b = $2$$ |
3cf85296-5e1a-4d78-897d-eac3424d5992 | differential_calc | false | null | Find the local minimum and local maximum values of the function $f(x) = \frac{ x^4 }{ 4 } - \frac{ 11 }{ 3 } \cdot x^3 + 15 \cdot x^2 + 17$. | The point(s) where the function has a local minimum: $P(0,17)$, $P(6,89)$
The point(s) where the function has a local maximum: $P\left(5,\frac{1079}{12}\right)$ |
3cfb5ae6-689c-4020-9a5f-eb65dc86e266 | sequences_series | false | null | Compute the first 3 nonzero terms (not necessarily a quadratic polynomial) of the Maclaurin series of $f(x) = \ln(\cos(x))$. | $f(x)$ = $-\frac{x^2}{2}-\frac{x^4}{12}-\frac{x^6}{45}+\cdots$ |
3d4817ab-4cb4-447a-ac9f-43a2d7a16970 | integral_calc | false | null | Compute the integral:
$$
\int \frac{ 8 }{ 7 \cdot x^2 \cdot \sqrt{5 \cdot x^2-2 \cdot x+1} } \, dx
$$ | Answer is: $\frac{8}{7}\cdot\left(C-\sqrt{5+\frac{1}{x}^2-\frac{1\cdot2}{x}}-\ln\left(\left|\frac{1}{x}+\sqrt{5+\frac{1}{x}^2-\frac{1\cdot2}{x}}-1\right|\right)\right)$ |
3d90964b-fc19-4336-ab11-3d7a1f653616 | algebra | false | null | Use Descartes’ Rule of Signs to determine the possible number of positive and negative real zeros of the following polynomial:
$p(x) = x^3 - 2 \cdot x^2 + x - 1$ | The number of positive zeros: $1$, $3$
The number of negative zeros: $0$ |
3dc0ac7f-8b58-4f46-a326-120c0d57d1dc | integral_calc | false | null | Compute the integral:
$$
\int \frac{ \sqrt{25+x^2} }{ 5 \cdot x } \, dx
$$ | $\int \frac{ \sqrt{25+x^2} }{ 5 \cdot x } \, dx$ = $C+\frac{1}{2}\cdot\ln\left(\left|\frac{\sqrt{25+x^2}-5}{5+\sqrt{25+x^2}}\right|\right)+\frac{1}{5}\cdot\sqrt{25+x^2}$ |
3e091f07-ec1a-4a3f-a368-62e4012f1399 | integral_calc | false | null | Compute the integral:
$$
\int \sin\left(\frac{ x }{ 2 }\right)^5 \, dx
$$ | $\int \sin\left(\frac{ x }{ 2 }\right)^5 \, dx$ = $-\frac{2\cdot\sin\left(\frac{x}{2}\right)^4\cdot\cos\left(\frac{x}{2}\right)}{5}+\frac{4}{5}\cdot\left(-\frac{2}{3}\cdot\sin\left(\frac{x}{2}\right)^2\cdot\cos\left(\frac{x}{2}\right)-\frac{4}{3}\cdot\cos\left(\frac{x}{2}\right)\right)+C$ |
3e0aa281-8701-4f9a-a1ce-c60021ecb125 | multivariable_calculus | false | null | Evaluate the integral $\int\int\int_{E}{(x+y) \, dV}$, where $E$ is the region defined by:
$$
E = \left\{ (x,y,z) \, | \, 0 \le x \le \sqrt{1-y^2}, \, 0 \le y \le 1, \, 0 \le z \le 1-x \right\}
$$ | $I$ = $\frac{1}{48}\cdot(26-3\cdot\pi)$ |
3e310e2e-ca05-4323-8356-e67852c3dc4a | multivariable_calculus | false | null | Use the second derivative test to identify any critical points of the function $f(x,y) = 7 \cdot x^2 \cdot y + 9 \cdot x \cdot y^2$, and determine whether each critical point is a maximum, minimum, saddle point, or none of these. | Maximum: None
Minimum: None
Saddle point: None
The second derivative test is inconclusive at: $P(0,0)$ |
3e35605b-4778-4579-a47e-2caf92caeb45 | differential_calc | false | null | Find any local extrema for $s = \frac{ \pi }{ 2 } - \left| \arctan\left( x^2 - 1 \right) \right|$.
Submit as your final answer:
1. The point(s), where the function has local maximum(s);
2. The point(s), where the function has local minimum(s). | 1. Local Maximum(s) $P\left(-1,\frac{\pi}{2}\right)$, $P\left(1,\frac{\pi}{2}\right)$
2. Local Minimum(s) $P\left(0,\frac{\pi}{4}\right)$ |
3e60b21a-39a4-4bfb-a47c-3798fee97a94 | precalculus_review | true | 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yEEQpIFiMEu04NtmMvF4qOg5OJeJjnA5INFDk7QYc2yBXqkKzIqFxlWTaXy65mBu/ZnVZvZZHAAFAqVyuV8g6T3BK7KTXQNM1x3C4muAYYO+6QYiWaJEk2xPI8t7vLwJoMAQCRJE2RAMBxIZZlAGDvssMYTNOgKJJlGY7nXAVExyza+v0333zj9u1bDz30kCgKi4sL9XpdVVVd1wuFQqPRSCQSPM9HImJA6Mlkst1uHz16dB+coAzTIAjEhhiO4wiis1K734O2bdM0jR0nFApx/F6NyUATaTs2TVMMQwcDcs/aEwMAw9BbPrdzfJK8ITva2tWWIb9v9ipDAAAMHbu8PZw8HVbgwKFlG6PLHYuvv/56vV5fWlp68cUXSZJUFGV5edmyrJdeeikWi128eJFl2fWJ7qNzZBcl6B61KgLUKb8GFpzdrWm31NAG39879qjwm2PXqGFfHLQ6M0AI7Yv/zEoue5vXBrn0mqn7ei6XO3fuXCgUkmUZAFRVtSzLtm1FUTRNcxxn/fDaY6vE+qz20/tlrR1h73lhT7Cm8PuT7SdJauhjIwQT/hvf+IaqqsGXzWbzypUrpml+9rOffeyxx0RR3P/F577iAfR82Tf0qeETj05vpTNnznT+qVKpxGIxTdNOnjw5NjbmfvnPhhf62BH61PCJR4ecuVZc5zjuueeesywrl8v1GaGPbaFPDQ8yeJ7//d//fYxxMpm832Xp4xOGPjU8yCBJcmho6H6Xoo9PJPpRnh5k9I+u93HP6FPDg4y+fqGPe0afGh4o9MWEPnYLfWp4oNAXE/rYLfSpoY8++uiCPjX00UcfXdCnhj766KML+tTQRx99dEGfGvroo48u6FNDH3300QV9auijjz66oE8NffTRRxf0qaGPPvrogj41PCDY0kW670Pdx7bQP5T9gGD95dedl1lC34e6j22iLzU8aPAvaPXvYvR/7Xzg/pWuj08M+tTw4GCNdBCEIQ44ok8KffSO/obiwUHXLcOam3L/OYWT7mNH6FPDA4LOOa+qaq1Wq9frBEGEQqFcLhcKhdwLo/q80EeP6FPDg4BOXlhaWrp+/frt27er1SpJkgihM2fOPPbYY9lsdvV1cn30sRn61PAgIOAFRVF++ctfvvrqq4qipFIpgiBmZ2fffvttwzA+97nPxePx+1vOPj5B2FVq6Cu57jcWFxdff/31ZrP56U9/+vz58xjjW7du/cVf/MUvf/nLsbGxCxcu3NfS7f/46HrF5icf7gXde4xdo4ZVd4/uC/an1/fjKs/dQ6vVSiaTjz/++Fe/+tWBgQHHcR5++OEf//jHd+/enZub25wa9lpDeT9m6b51XZdhspftiQB/cqhhf+Ha4fZtrOGOn3uck1evXvPqNFhijPP5/De+8Y1sNpvL5QCAIIh4PM7zvGEYW1ou99qE4Sa/b72GEcbY2a/sVuq1xiS0BxkBAAa05/XaPWpAsJ8k/aAr2rd3QXbwOZvNZjIZhJCiKPV6XVXV27dvLy0tPfLII+6dl11nfueXD0zLYgx47+fPSnb+hz1uQAQAGAHee8rbKTWsjCqMVVWt1xs7L9NG8PMBWZZ13Wi3Jcdx9i47F6ZpqpoOAM1mi6bpvc5OlhXDMGVZpigqqO8m2OiZmzdvvvTSS7IsXblyhWXZRx55JJFI1usNVVUWFxdlWXYfm52dLRQKr776qvsrx3H5fF4QxN2tlAtZlg3DlCQZY0wQe6sFcBxHVVQMTqvdNk0LABACjDdsrp0AIVAUVdN07ODO8e/muBeQZeWToWsI2EHV1Eajvkcelp0rmywrhmFIkmSa5l7k1QnLstxr6ZvNFkXt+f5L13Vd1yVJDkZV7xJ+55PLy8sTExOmaZimGYvFdN2s1eoAUK/XLl++XC6X3YdnZ2cbjcZrr73mvpVIJB555JGBgfxejDxN00zTbLfbpmnutWziOI6u647jtAhJ1wz3S7998E5q13kvufsNQsgwDEM3bdtpNJprHtsJ1p+FQQhjjBRZ/QRQQ+CHC4AYhgmHBYT2aEHAbithDLZtWZbFcRzPc3ut3DJNU9N1AOB5fq+lBoSAIAhVVUOhUDgc9ped3ofyypOnTp0Kh8OWZU5NTf3yl7+8fPnS4GB+eHgIAB85ciSbzTqOgxC6du0aAJw+fdp9SxCEVCoVDof3YuQhhGRZ5jiO53l/N75X66rjOJquO47D81yIDa3+446oAWAtNQAgkiR1w6RpKhwOr8llZ3X0ZpafjqvRQKZpGaZxz4n2iF1YBn1WwxzHxeMxALSXuh8EgG3bMgxTFAVRdEXfPaQHXTdcqSEajbAss3cZuSOAIEhJkgSBj8djANBz1RDGGCFotdouaR45cuTIkcO2bZdKpcnJycuXLz/22IV4PBaJiLFYzLZtAMAYv/322yRJPvPMM24qBEFwHLdHwhFJEq1WSxCESEQMTny5xd512LajqIrjOJGIGObDwRzbpey8AR/sUGSZVjUtxLLxeNQlgkB14z65w/wwBl/eAYzBMIy21NphmltidwaBy6AkQezDbhwASJJACFEURdN7LuHbtk0QCABomtqH2lEUhRAiSfLeqnbp0nvLy8vnzp17+OGHCYKgaXp4ePjQoUMvvfRSs9mkaZqm6VBoZRXleZ5l2VQqtXs12BAkSQBgmiZpmiIIIpCW98ImQhA2QSIEiO4YJLso5MNqgw5FkSSBSHLt+N+V4/BuFh0/gSJJdMA3FJ2F3l/zv7ez2IfDQh0nmve8gh0j6R7zmpqa+vGPf7y8vJxKpYaHhzHGuq5PT09TFCUIwur+Wsl0f85c+UfF15pI98pWihGgVWqvXeGFNYkEY8MdjWtaeFfswasTBM+H4oD7NayqP9pnZ7e9Mx2vAgbYN2eunVfn/PnzP//5z1966SXDMM6ePYsQmp+ff+ONN06dOnXixImu9vY10Rz2EiuUty85Blqw3Utxw2JjhFZacgP62JV8/R3KJ8mvAfbbbfBBMcDvJh5++OGvfe1rb7311u3bt+fm5iiKKhaLx44d+9rXvhboGv85Yc9t2/cHnvPY3uIT6g3ZR3fwPP+Vr3zl9OnT09PTpVKJJEmGYU6cOHH06NFEInG/S9fHJwl9anhAEGxHs9lsPB4fHx+XJAkhxLJsPB5nGOaBcXPsY3/Qp4YHBJ2OMQzDpFKpjewO/UBPffSCfmyPBwc9mso6vNT66GND9KnhAUFgNuvxyX0oUh+faPSp4YHCRnM+oIw+L/TRI/rU8CBgc5Eh+GufF/roHX015IOAzWOH7GVkkT4eWPSlhj766KML+tTQRx99dEGfGvroo48u6FNDH3300QV9auijjz66oE8NffTRRxf0qaGPPvrogj419NFHH13Qp4Y++uijC/rU0EcffXRBnxoeEGx+5rJ/CruP7aJPDQ8I1tyb0skFncer7k/h+vgEok8NDxQ6I7ivuTGhM3J0nyP62BL9k5cPGhzHabVatVpNlmWEEMdx2WyW53mCWFkG+qcw+9gSfWp4EBAEYnAcZ2Zm5uOPP56YmKjVahRFcRz36KOPnjlzJpVK7cN1vn08MOiPlQcBwQVH9Xr929/+9uXLl0OhkMsFV69evXz58vPPP//ss88GgWT7MV362BJ9angQEEz1d99994UXXkilUl/84hePHj0KADdu3Phv/+2//exnPxsZGUmlUu6TfV7oY0v0qeFBQDDVVVV99NFHP/WpT/36r/96OBzGGJ8/f/6HP/zh9PT0wsLC448/3ieFPnrEJ5EaMOzDtV73D3jV/1vM5DUB5h9//PFjx46l02me593v3fuyDcM4CKTwAPfag4ddowaEd7nn1+2HMfYmCsbeLbWAMfanhcsXCGHccRlmT7NrS+zqlFpVJPdOdABw/8cIkFc77wdG7o3PHe+vbpY1d17ncrlMJkOSpPu9YRgffvjh4uLio48+Ojw83DWF3a2b1xcYVufh9g7GCLvdBx3dtKrHDjjwmquRkftVMPb9DvUvrXWfwft9HeyuYKfU0DHOsGVZmqYB7OpNtcFUwhgDth2ot9S7c8VSpV6R8chAKh3jSDIwy7nWfOSPN7yTwrip6LpumiYA6LrudvyOCDCYNZ2iD0IAYNlOra3NL5YXCuWsZOs2GY9wJOGW3q/C+qp0eDYFNbUs2zQtTVOnp6e/+c1vchz3+OOP5/N5TdMsy2q325ZlueJGs9mUZXlubs59kaZpQRBohrn36nmlXGEJQGBZTlPS55Yr0/OVukKNDNqpKMvQ1Npy7x4c2zZNE2NsGIZrl8EYoHOO3luWATUEsx7jtmLOLpbnl8s8x+qYTsfCDE0CACAMGAGgHfFC52jz0zFMex9ub98pNXSuDZqmNRoN2Jtb5zFgx3EWyu3Lt5bev7lQqDajIv/YqeGLZ4bySZHxzHKBqt5fc+8V/pvYND2+azZbNE3u5JZiFOyFEIHAcTAg5Lgz37BwoS6/e2Ph/evzpUYrmxQvnBi5cHJwKCUQiNzujenYwc1mc2Jy4p2337p27dozzzxz/PgJAGg0Gu12++bNm61Wy6WG2dnZarX66quvAgDGOBKJHDt2LJ5I3lP9IJgxAStgDA7ghVLrw8ni+7cW55fLUXH60VOjT53KDWUiLE3vlmS3thwOVjUNY9xqtXXdWPWnnazh/uBCABiQjR1VM9+/VXj9o5m5QpXnmIcOL188NXx4KE7TJIEIAAAECO+WPO2lpSjKPsghu6hrQLZlG4YBAPgenSxXjxKPoZH/i1NrKj96/cYbV+cLVcm0LEBoeqm2VK595akTY9kYRRLu7EOAsHd7OrrnFkQA7hXsluXYtg0ApmlibAMAAHGv1ID9TQIB2LaBIJCNALADS1Xpl5enfv7uZKUhm449tVSfWaoXqo3ffvpEUhQABcMZA4ZVOybvLwEjYgc7jUbz/ffff/XVV3RNfe6555599tlMJmNZNoClqmq1Wq1Wqy41SJKkqmqhUHA51TRNWZbDgnhv7YYBI78PkSu4YVyTtF++e/ulD2aWqpJh6gjq04VGrV79woUjh/JJRCAC8L0OmA3hOI4rGRmGiVCQuMtWneNqW8CAHQch5EmUSNH1D24tfvflW3cWqqphkiS6u1ibWSj/i2dOHR1JshSNEcKACYx2sEi5mxXCFzgxAmRZ1j0n1zt2Uw0Z4kKxWAwAdkLLG7yLHQe/fGX+tQ9nZ4ut48OJh8aSizX9lSvTkmLkU8mBdDKVjLqPEhgwcj2B73EIdBQGDMPUDQMAIpEIw3iyyb0nuVJBbAMiAAOAqplLE+Ufv3l7tti4+NDwSFqYWKzdWqjZH+HDw+nffmYAbchxK82F/V1Xs9V87713f/qTnyCC+N1v/M5TTz0VjUZJ0utojuMee+wxVVXdX2/fvr28vPzss8+6v4ZCoXQ6zfPhHVQwIHjH3Wa/fuPma9fmZov18XzioUMjyxXtzetzP3tXG8tnTowPh8Ms2tE63h2247gbwEhE5Diuo2g7zMjblyAA28HNQuW7r914/05xIBV+4tSAplsfTZVf/WiOosj/Z/y5WEzAyJ3WO8vU25hg8OUP27Y1Td9ZRbbGblIDy7KRSGQnKWykIXMc3Gzrv7g8tVBunzyU/eoT4+cPp8oyNk186dbcKx/cfejw0LHRPEkR4C5cns5hh9QAAKBpWqstAYAghEMhdmeJecAYe6IhQgBQrJc+uluaK7fymdg3njszFGevz9XRu1M3Z4q/vDz92889InAhguhSjzXN5S77r7zy8quvvMyyzL/6V//qS1/6Esuyq5tUTKfTwS8/+tGPTNN87LHHdqVerqCHg50TxuWa/NrV2cnF2vhg6refPvnQcKRlEFVJuzlb/GCi8Oip8Qu5lCtH7U4BfNi23Wy2HMcOC2EhHPZLt1P9q7dsu2oaWZ0rK+/dXGYo8rnHDn/qxIBlo3Rq8Xsvf/SrK3d/45lzyUQsKobcPt55BYPCY4wVWdlhar1gl42XO2z9jd5VNOPta9MfTy6GGPoLT5z49LkhBqyRkSQX4uf/f7Xr06VLN+dOjmeHszGE3JGJENrmBn2TQnX+twvACAE42JVzbdv5eGr5tSsTIs98/Zmzj58e0+TWU2djqkPPFRrXJpffvjr7mfPj4VAX1eCa5kII3bx58zvf+Y4sy1/96lfPnTvXaDSC8SSKouvpsHeHrFxx1213jMBx8Hs3Zm9MFWiKfOrMoWcfOWLIrWPjma89e7b243cv3Zg7Mz7w0JFciCEAyN0tSVCiTr3Qzu0ywdk1ALxcbb343oRp2U+eHvnco8cGIjTLhmLJ5MRc8dLt+e/86sPhXPyh8ABB7M7ACZT9fkn23BC8oz3e+rG1K1axNclijOtt+fuvftiS9Asnhh87NZKJiwRBhHnu4rlDj5wcJknyveuzH95ZCAyB3k53N+TUTkPhjhMLxqo7gxAALtba16cKc8X6cCbyu59/OCZyBIHSceGJh0YePz3SaCvffvFKo6Wsb5Ouyb/66qsfffRRs9mcm5v74Q9/+K1vfev/9XHjxg1Y3UFrOmvnp7YRRq590lXdK7rxq8u3SzXpzJH8xbNjmbhAIGBp8otPnjw5NtCWtasTi3cXynukUcPeONjVNAFhBICwZppTi9U3PrrLUORvfObM+GCSYegQS50Yzf72s2dZmrl0Y+72bFlS9F2pW0e/7J8n646oYe2qtbOibJSsppsLhca71+cIRHzq3KFjwymKIjACChFimP3yxZNDaXFivvzhncWWpGFA3j4C7bKfxe7BmzwuPr67fHVimaHph48Mjg0mKRIhjGmSODaSfursGAC88dHk7HJV081VSWwwPmzbHh8fj0Qic3NzH3Xg6tWrpVJpkzLtjgM1Qgi5qjdkmM7McuO9G3OWZV04MXzmSJ6iCEAYEBpKR548PZKJCzfnSm9em9kjO1xwPH030/RN2sWadH2qUGnIQ5nYkw+NJiJht/VSMf5TD4+fGstJiv7BrYWFUnNXRuF68fATZaHYKxEH11vKB7cWyg35+HD6oSP5VCxcq+kArg0JffrhQ794+9ZCqXFrtnhrpvjYQ2PBi7vibbKblfJVWMi3pJimfW1q+c58OZuIfPrcYYYmNYQAYYQgLvInRjKjucT16cV3bsyO5pODIcY3vQWy5dq6feELXzh37pzriLEG7pGKjbDbaxFWdPO9a7OlmjyYjp4czWTigiJLbk4MRT52evjtq1Pv3pj/8M6Sqpm8t13aTX0k2q7Jt1dgBDBbqF+5s8hQxKfPjmcTAk16o5+myXw69uufOjmzXLl0Y+biw2PHRtO0Zzvb5WLsdoJrsWvU0LkS7iIcDMvV1qsfTNg2/szD40OZGE2R4E16DIDSMfH88eFrd5fd3nrs9NiKrw3anaG2V52AodSQphcqLUk5eyT35NlDCAMAgRHCABRJ5FORT509dGN66Y0P7j77yNF8Krpi2PX/X6Pfeuihh/aosD3DteuBJKsvX7qt6da5Y4Nj+QRNui4hboAZdGwkMz6Uevf63OxSdXK+dPboEMbYNcKCP6V3o/fw7jKeWyIb47nl+o3pghgOffHJkyGWti0z2CvyHPPFJ49/8+eXpxcrE3OlJ8+MZmLh3Z4bu+163A0HNcqT7wytG9Z8sXnlziJJwLOPHk5G+cCjBru7Y0CPnR49lE8Wys2rE0uaaSHfr2gfPMa2D+QPfQQIbs2WF0rNCM8eH83m0xFXB+FaqjDgVFz4zCPjBKCPJwtL5ZZmWoGLIQp+HjhgADBNp1yT3r+1YJrW+RNDg5kYeLoMT1sfFfijw+mBVKRUb7/38RwEytEdOADsA1wptNZUZpdrtaaSiosXTg17vo/g2ctpihwfTJwezyOCuDVdmF6oHPBKbYSDSA0YwHdLx5WGNDFfljRzdCB+ZDjpKepd8c3zN8ZHhlKH8gkHO1PL1emlSrCiwoGMhoi9HxhjuDqxtFhpDaSjJ0YznqHVn/aAIRxijwynR/IJSTUm5svVpuxtRwB7Br9Ob+sDAY/RW7J2c7pYayn5VPTIcCoihAAwQhgQxq6JE+MTY9njY9laS333+qznKYUCvaFrgT6QgeownlqoTi1WGJocH0omozxJEIDBV9RghBBLU0+fO5SKCTdni7dmSrA6bOcnBQeNGvAqYQmjpXLr1kyRD1FPnjkkhDnXvI8xwkAgQK7AGOaYo8OZ4Vyy2lLe+3gW+76wCB3ESGe+KsuxbPv2bKFcb+dSkWMjGex6NLoFRwghRBAoJnBPP3IkxFIf3FmYK9SR7/ninb/aF3XUduCWB1Wa0qXb8wjgiYdGM3GRJAi3qO6WASEMgA8NJo+NZizLuT1bLtVl23a8U6ReOj5ZHCS4Vq+pxerMci0RCZ07mscYIyA8tu6wkz5+aiQTDy9X21NLVUnRYfe1OXuOg0YN/l4BEMbIdvBCuXlnrsSz9JOnR0IMDdgTGAhvhUUAiEDo+Fj22Gi23lTeuz6LALseyQds2njwV3pUqktL5aZj24Pp2OhAAnmbIMdnRgwIh1n6s+cPh1jm+uTyfLHh2E5g/MT7suHcHlx7rOOU69KV2wuIwI+dGIoLvD8rEHZpATBGKCbwI9l4KhautdX3b85rhuUtu15Cnqr1gNUQDMueLdSWK61EJHz+2BBCGLtbQNcZ2tM0o8PDmbGBJIHQXKE+u1TbSGQ4yKLEQaMG8MRKQIBQW9Vnl6uL5Xpc5B85McJ6mzpAnic09jdxeGwgfmQoZZjWjalivaViBw4mLwBAsJu4MV2ot9V0XBzJxgSeBuwgAOz5F3vOsSxDnT8xHBP5cl1eKjfbqusei9DBDODmHv7RzMVyc3a5yvP0qfGcyLsupBggOJqEECCKJAaSkcODSVU33r46repmt3ly4GpZrktzxbqsGdlE5MiQG1AP+2otjD2CRxxLnxjLpqLCYql5Y7qANthTHMhe9HAAqQHAP/uwXGnOFesY0EguMeIeoFqlW3SCT3GRG8vFEpFwpal8PLmkm1ZgwzhA6LDvOhjev7nQlNSxfGJ0IEESCIBwZw0OVAkABElkE+JwLk4QxHypvlRtusThJXcQ6Q9Xm8rsUt207JFcajATZWkqiGfg1srXtsBAKnLyUE43rMu3FlTdCzbjbyg6/jtAwNNLlUKtLfDcWD4ZEzm/jH4VfY4AgOOjmVxSXK62bkwVHMeBg00E63HAqMFVY/kNOF+oL5YaEZ47MZoJMVSHp4err1qZ+DRFDiQjh/IJzTDfuzGrGhYczKnjzwzLcT66s9iWtEMDiZFcPCgs8g7SePY7hICiyFNjmUiYnVmqzixWD16VVuBu40q11t2Fcoilz47nw3yIIAjwKA9hcIIjyhhwOi4cHU7bjnN7ttRsq5btcX0nfRww4Im5crkhZxLCkaG0e9jX81PxtFsrNtdjo5l8OtKU1LtLFXXdaaiDvJVwccCoAcHKjMcwV6wvlpoxMXR6fAB8q3fwz1X/+DoFlI4LR4bTumFdvj2vGftxavUe4K74Dkaqbs4UqpphjuTig+lY4AjlSgTIFw1cwnjkxGBc5GaW6tNLddyhhsQHbSuOEEJQqLXvLlZ4hj5/fKgjXgsAYASOpzrFCAAEjh1MR+MRriUpM0s1WTVWJ3e/arcJL6E78+VqvZ2Lhw8PJT07tK89RSt+FAhjnEuJg+koQ5HlhjRbqGMvupXH+wdfgDhQ1IABIDhfZtr2fLFZqLbjEf7hY0MrzLwiUnuhMtz3csnIqbGcadkf3y1IioaxcyCXHYQRmJY9v1xvy1pE5AdS0Ug4tFJUN94bClyZEACcOz4cE0OVurRYaqiGDl5MCv/PBwYIsGU7xWprtlAPsfS5E4MsTfqEh329IvJJHkiSiEf4Y8MZhOHjqeWm7B4VxyvuDbsWBKV3YC9T7H1Y4QkMsmrOLtdakppNiONDfsAbBACBetiTeRFCNEkOZmIDqWhL0q/dLXhOEcjXNa0wxQHFgaIG35gNAAiX69JyRbIdnE9FRgZim7zmHpONityhfCIWDpXqymKpoepW4Fd3kIABY80wP7y9YJj2oXwyEQl7bkAbYyAZySVEBFCstRbLTQA/zNABU6dgQPWWslxpqZqZiIYPDyUpkvBHP8JBYRF4lmWAaJg9fTiHEfHxdKElqdDhq+a6Qe0793lncDx27ohD6gBeKjerLZmh6VwqloqFPQrDKOCTVbtYDEOZ+GA23pT161OFQEfpjXMv1s2B4vZVOFDUAD7tYgxocrFSrkupaHg8n6TIrcqJEEkQMZE7MZqxbXxjptiQNDhgiyqANxpU3bp2d1m37NFcPB7hYasZThHE+GA6GQ2X69LdharLn2hFijooQIAXy62lajvMsUfyqXCIRcgLneEHVUSrtwk4Gg6dGc8DoFuzpXpbdXz+8MNt3B/iW1GH+m51GDDGMDFXlhQjl4oMpCIkEThfrHcw8QzMQ9nYcDbaVrSbMyXDc9wIDgAGIbEOKA4UNWDkG7QxwJ25UqXZysSFscGtQxW6/Sfy7PFDWQT4+lShKakHr+G9+awb5o2pomk54/lkMsptPbsRHBlOZxJipSFPL1Y9t4YDxgsuliutQq0thtmjIxnCjVXgLv7+/FnjwhnmQ4eHU+EQWai2ynVZ95VEHeEJ9r8bccdP8PWLCDvOrZmirOj5lCvEee3vboO7ekPnkpHBdNTB9nyxXqnLto1dH103WQSov6HYLhB2nLvz5WpTTsbCI9n4Fk/7HwSePTqSRgjdmik0JdV3fDpYcBwsqdrEXMm2neFcPCpwW78DcGQolYmLtbY2V6w72DmYvACAFoqN5XJT5Bnf5o8ChZu7wq4omQEDIJom03FhKBO3bGe53GxK2poE972aXckIASAHO3fmSpJqDGaiuVSkIx6It0Fa/TwAgMAxA6loMhZuy9qt6YLuR4LGgZXmAONAUYOrYQSMQdOM2aVGW9YzPVBDgDDPHhvO0CSaWarXmopl2Qds+iCMQdXNYrVdl1SOIXNJMcy5HkGbFRQDHBpMpOOCpOgLxaasGvdhD94DbMeZL9YLlWY0HDo8nHLNTauHP3L3iwFDEAhxLH18NMNS5NRStVyXV9RNgO8H/XVMeLxSZozBsJyJ+ZJqmAOpaDYh+PVyAoUEdKgV3f9IgsjGhUMDScMwP7y9qJsWCpTMnrBxEPvRxYGiBgDwLHPLNanSVFiayqUiqVh480OG7vjDGEIMPZSJZeKCpJmFqiSp+gEjZowQSKo+s1QHAkZz8bjI0RS55QRAGEcFLpMQGIoo16W5QqND73WA0GgrpXpL082YyI0MxLC/0euYbx1ug97vwNDUmcM5lqEmF8rFehu7+yXcdfXeHwTdEeggwXKcYkMuNWSaonLJSFzkPdemQBnsXyOGA80lAgDIJISjwynDsq9NFXXTXsnjvuhYt4MDRg3Yw625sqTpmYSQS4oURW7VhF40NZJAPEcdHcmwFDmzXKs05H0pdK9wdVmSakwv1xFCx0dzvsiw5TTAGOOBVCSfikqKdmeu6N2xccB2qgvFRlPSogI3kI4JHAsYAxCBCxcCQOBg1BlOCiMAhiZPH84zND27XK81ZVfWOBCqe8+oghCArps3pgqmaWcTYioWZhnSDVqOEeESwgr1IQTgBNM+GQmPDSR1y/747rJhWOCxiG/OOAC13AgHjBpchZXjfDyx1Fa0XErMJAS8lcpgRdGLMUMTp8czLE3OLFfKDelAzR13SkiKPleoI4Cjw5kwx3i12/RIP0YEAsinxHw6IqnG5HzZnT6BFuyAYKHYbEpaOi6M5hI4OAsTVC2wYnq/IlfvzFDksZEMQxGVllRrKYZp+2vvfceKGVIzzBuTi6ZlDWcisTDrCwXI545OJnPVCF75I+FQPhWjSXKhVCvV24Zp+04rB1Lw68DBoga3oTGGm9MFWdEH07GBZLSnk8du7yDE0PSZwzmWoeeKtWpT6eyyAzDaMAC0ZW1qoUwgOHEoLXCsX/LNXnMtutlkJJuKtBXjzkzR95hZ1TRdK7gftfY1+rOFWr2tJKP8SDbueQgGzqrga+sCpvDd1yiSyKcjiQhv2065ITXaKtxfg38wZ7HnuQkIdMO6M182bWc0l4iLXtQm77rLTmWDV08iGHgsQ6fj4WxCNG1ncr7SVnSfLNHBFhoOGDUAgOsRNFdoGJaVT0UzcXFravW2fYABaIo6PjrA0NRisVlpyI69cgTrIMiopoXrLWWuWKcIYmQgzrG93y6JcslIPhXVTWu20JA1C0PnPawAG1Rwr2vt3y+DAeGpxWqtpabion/G3DNKdGwp/C9Wl5ChqSPDqTDHVOrtSr0NbhCX+xUcqSMQNcaeeKCZ1sR81bKcQ4PpRDQMXsU3CjC38i1BIJEPjebiAGh6oSq7Z2fv/yq1NQ4WNSAA23bKTbnWVhmKzCXFRJTvXU2NASgSjQ4kRI6RVaNSl9vKnl/ysx0gSdaK1bZq2GI4FBc5mup280y3FwFwTOQycZEmiUpTXSg1LHuzcyK6rlcqleXlZU3T9lRwQP65FsOyFktNWdWT0XA+HelQQPakUDw5lo2FQ6WaVKi1Vpbg+zaDfP8sQIDBduy2os8V6oBhOBuLiiGXcpEvE62W3tYizDHjQ0mE0HShIqm6p6JcZco4iDhY1IAxNkx7aqmmG2YmJqRjYZahtmSGDmkOEwiJPDOcjTIMVW7K1aYMB2Ir4aHelperLYYih7Mxlia3taLTFJmIcOmYoBnGnbmyYbrUsCoJV4mrqurk5OQ//dM//cM//MPi4mLXANO7C4yhXGvXJYWmyGSUj4RDq9f8LeuJjw6lRS60VGktVpquKH+/duK+qBNshbCsGvPFhqTqEYFLRcMsQ3buHzy9z8Z1FMOhE2NZhPB0oSpr+mpnjYMyMtfjYFEDQkgzzBuTS5ZpHxpMJaI8rHae2+xd1wMVIQxwZDgd4dlyvV2steFgbCUAAAA3Fb3UaHMM+dDhPE1RGPcUrMlXK0AyKozlk6Zl35kvGqa3V+o8qIMQkmX57bff/t//+3//9V//9d/+7d8uLCx03p66iyzpuj+7IjfGaGqxqup6MhZOxcIUSXhWIz8W31bsgMfySS4UKlTbhUp7xafhfjitIc8QuaL+bin61GKFwDCUjQk8QyD/YIh/ZMzl5I0SjIRDp8fzCMPsUk1S9MAmGmy3DiYOFjUAgGaYH99dNmx7LJ+MRwRPob25hSLQ/rjXSCJibCARDjGFSnOp3DxIsbfc00fNEEOdPpynaapHRZQnsmKUjIbH8knDcu7MlQ3T9jV73k+3Ru++++7Pfvaz2dlZnueXlpY0TXPjiLgCxW6xJMbY08sjhAE7GN9dqiqamU2IqZi4oipAWxOfW8V8JsaH6JaklRuyolveAYr953R3tCHvCnJ3XyEp+txSlSTw4XycC9GupclXsng8sklJWYbKpcREJNyS9FKtraj6SsyaPjX0DKwb1s3pkmFZg5lYVOD8C897GV4Ye4EMYCyf5LlQsSYVq62DE3sLY1yut2eXazSNRgfiNEGgYN3d6lVXTx4TQ4OZiG7Zt6ZLumGtqZRbo1KpNDAw8LWvfe3zn/98Z9a7W5eV1sMYAXYcfHexJmtWNhHJxATwnZ16JAYMKMIzyShPUUStpZZqEg7ofp97CYEXqbzj/JqimoulFkLE8ZF0mGPc1T64VBUhYvOxhABYmjw6kqVoama5Vm0oAAfccAlw0KjBtJ1GW51drgJAPh2JhEOw4lG3NZAfgn0snxA4uiFp1ZZi2zYcjD0FxtBoa6W6TFHUSDZKEYQnkeItqc+zp0XCoXxKxNieXao0JdV2VuTY4MOjjz761a9+9cKFCxzHBaIE8rEb1egorO+9gB08OVdWND2TEFKxsP9Xbyux5aYJARAEGsklEtFwU1KWyo372FteQf1jfhhAUo25UgsT6PhYTuBWbkvvvZA0SY7n4zRFLJSatbYaaDEPjhZsPQ4UNWBVM5crLU03I3woHQtzLOVbgHvsBY/pB5JiPBIyLavWUiVFPyAdoKhGU9IM0wrz3GA6RpIEAGzt1eACAcLAsXQ6Fo7wIVU35osNRTMDmSiY9qOjo2NjY6Ioeu/tCSfi4AcAwhhppjWzVNENKxMXkzF+ZcV3xZ3e1CnDmWhC5OotZa5Qu9+q45VGs2y70ZYXS3WSJEdyCY6lOxsUu96NG5y8DEBR5Hg+wVDkYrlVbysd2dz/FWsj7NrFdu7S4W5r7xmyqi9WmpiA4UxUCDEIwHHsIPngMYwdjB3bdlZl13FtC0ORuWSEDzG1prJUaQk8652795fn3jvEcRyMHQBwHLvH2q1Y8IMsEQYM5Ua72pQZmsolxBBDYYwxdgOiYexeQO9nh/GaqnkH9hCCMMcMZ6KNljK9XDt3TBU42n/Eax+apgHAtm1XueD4CB6zLCv41bIs27ZV1Q2vBAghiqIIYtMFw4vj73hmBIRNC0qNdkvWGIpMRjg+RDuODZgAP/4t9lsSwMG4SzNiAAROLilGBW6uWJ9dqjrYwRgQ3ONwchzHwXZQ/e2+7mkhEUYY2pJarLU13UjEhagQIgnkOHbQw563F3YcwG7dumpIKAIdH0szNLlUbtaasuPYnqc7ONvkbgyAHGc/aHOn1LCyXmEwTVOW3WML98aFqFpvzyxVEAHj+RSBcEdquDNNXTcsy9I0jaKC8mPwzxW4skNcDIk8U62378wsD6bCyJePtntBhWEYpmECgKpqlmVv+TysxA31+w+7Zmw0t1wt1pp8iMklBFlWOx2BAp2XpmmWZWuaLssrawvgIFgIJgEO5VMfTxamF8vVRjPCBaezVi1mqqoZhokx1jRNURSECL86eqlUMgzDpZJKpdJsNm/fvg0AGGOWZVOpFMfxm1YQAyZw4AaIsKrbE7NFy3aSUZ5jSFM3TB0AEHjE5yGoGkmqBBFoEbBfPScWZgSOaUn6QqkhSfJO7oO2HccwTOxgVdV80RivWWA2q6DXKRhhXKq0C9UWRZP5pOhYpqKoqx9GAFhVVcs0DYKQZcWnhmDQYgxg285wRmRoolRpl6pNSZIREJ7SfIvCBK20UjZdN/fhVsMdUYPLCz47YEmS/Jva73GfMrNQuTlVQIhIRUKy1C6VLF8TtappFEVRVa1RbyqKq9GBjr9iAAIAcSTwDFltSrenlh4aiQCQOAibth1nGsuyXIaqVAiSJHt5xacG5Lu2OA5CAMTU3HKp0mQoJLCoVCwDClYzN84JBgBdNzVVayJkmlYHIa4wiKrIA7EQIDQ5V5lfLIbJFTtFpwxeqVTbbclxnGazWS5XZC/sItTrtTfeeL1SqTiOgxC6ceNGq9X6zne+gxByHCedTj/22GP5/OCmc9LBQPmHkREgaMnah7dmTNPK5KLY1MqlCvZkOOy3NgCAruu6bjQaTUVRV88IDIAwxjToLIkVTV8s1xcWl1mGwkD23lOriug4kuQdrqNpycumVwON19oOYALwzHx9bqnKUNRYJtKo1x1jhbKDBA3DUBRFN4yuqXtGD8sKs9SSocwslO/OLETCLAZAmOw9SiH2Q3tJsrwP6tkdUUNgNgMADEASpCvN3nO5Fd2aWqwiTIzmYhGe7UgtULYBQkCSBEGQJEXSNAWrFwIEGAMBAKMDiUSUn1iolVoaTdMYCAh81z30ptpE4DICRZEdQkpPr3rUgBwHCADUkI26rAs8e3gwSTMUgIM9acG9BRdjDLbtEARBUSRNU3idaIoBYiJ3ZCgBCM0u13XTcZtovRWGpimSJBBCJEnSNE37kZ1Zlo3H49gPW8rzvKZpqZQbdgVisVgoFPKbfSO45EtgVz5DGDt4arlu2U4uFYlFeIqmXImCAORgJ1gYbdtyy0NR1FqVKAYMkIzR6YRI0WRTNuqyMRzmOhb87cFxMEmSgDFNU0Hdt2u7dRmiLukLxUaIpo6PprkQQ9PU+tbGGBMESZFkkNd6MAw1mInPl+VKS6219WQ8DBgBEL3Xzh8PiCRJ09zzmOm7IDV4HwBFImI+n7/n1Czbpu9Wa5JKIHT2xOih0TzDeNIyWj1LyuUKQD2VSkQiYpdSASAAE9GZd+9+OFmUdNst1coSvB17ua57sncul2WYXo88rNZoeDlbcLulmIfyiUdOj+fzuc4iBWi12qZpxOPxVKp72DvDtBWLBHCqbYUKhdPZDE2S6yuFEESjEYIgkslkLpcTBM/tP5fLjo2NBtRQKBTm5+f/5E/+xH2LIAiGYXoSjnBAtNgCpto2bIxG8+nR4fxAPuV+v4aKW62WqmqpVFIUhbXqDL/0I/l0Mhq2MejADuQGUI9+5Otg246DHew46XSK5zffH3WtXKAiArhZqkk6y5Knjw4NDQ2EmC68KcuK4zihEJvPD3QnIAwYwbHR3MdTRd0BMiTkB/L3vIISBaKolu7t3d6xU6nBbQi3LQiC2Oa6ugqyZjYkzbScpMgPZmJciEHujtRbe1fakSQJgvDWH/+7lcno9ms2GU1EBNOyKo22bjphjnJLCmv3QVvAtm13HK/ObhP4Q2plM4ARgO049bbckhQ+lB1IRUmS9PYBqwvvV21tS3o35SIgSDIZF2JiqCUb1aasGTYnskGlNE2rVquappXL5Xq97jhOqVSan5/jeT6ZTEajUYQomqaDirMsyzBMNBrtoV6r6+ipTT2NwmKpYTt4dCCRigkURblqe0+/4zcGSZJB1VZTgxtVlsCAE9FwIsIpqrFUblEUidy7TbcPhGyCRBiInnttdfUwIOQAJmzsSJpZa6vxSOjoSCbEMBTVhTddAc0d/xtTAx7PJwWOqTfkelP1S9VT9TrSxG52+xAsfadqyF20jbUkrVSXKJI8NJTiQwwR6A1Xtqsr2W6SszvZeJaJR3mOZSRFW642Dw8mUBChGKG9DhYSTHjP8I9xWzGakoaxEw2HYgKHVgtCHX3fvVS+HQMIBBzLHB3JfXRncbnaakpqXOSD15vN5ltvvbW0tNRqtSYmJmiavnz5crlcZhjmU5/61IULF3buELmiZMUIEFg2bklaodwgEB7OxCPhEPIdIVfrSVa3zdo03TKhTFzIxIWbjeJiuYXBvTz3XkuLEdyrgcPTIyKsqEatKSuaMZKLDWbi5LrI5msmLWw0LhEAwFguLoSYcl0q1dv+Kz3Vbk2a/g5+b3GA/BoqTXm+2GRocnwgQZLEGpX7use3UF8TBEpGuITIqYa9WGq6gUM6vHW2NeDQltmtfrjLl8VauyXrAs/lkhF/R4q62e63zoumyOMjGdo1krdU6Bg6mqYtLi5OTEwsLi6SJHn+/HlZlmdmZiYmJmq1WueTgStUb5XqUkfXH0NW9YViQ9WtqMBFBZahSABfe+I921mdrlVDwX+5ZDSXismaObdc37ESvvcu2+h1qDblakOmSCKbEPkQs3GMmV7cydBoLs5zbLWllBqS7dwL67mdhjc/6blL2AW/hsBCsUMeqzSUhVKDocixfJzyqcFVaG0ZQXSNaOGWKBsXc8lIod6eK9Q7bKy+VrO3rulUNvVUjW7JYuQFR4uJfDYpgrdBwI6/p9hyYOEOOxdNEqO5GE2RS+Vmp/8MAMRisSeffPLYsWPrUzh8+HBHat1lh15kCrT6MVk1FkpNIIhcMsIytCdR+BYXtPbV7q5MQd8ko3wqFpZV4+58yXYwubmHxZ4DFWtStSmHWXogFUGufbyDW4OtdOc1PBu0HwZA2WSU51hJN6tNWZb1iMDBVmJR5+Z3Ve/svWfDLlADunf5ZlW7tGS1XJcYhjo6kqbJQHO7iZi9Rs0XOBB4omwqLqbjkcnFyu3ZEgYH3DB+91JIL/GeX/BlyxXlBy5W221FFzgmGeExYEAEdoLirBSq+4z1pHOvfhRJjOUTDEUtlZuu1BAgGo0++eSTfoE7lMSrP2w0/3sSIrBnTnGf1Qyz1JAJhA4PpfgQ6/4RBVczrfMw2zyLSDgUFVjTtMr1dlvSY5HQztjhHieQ56SGoNJUapIa5pihVBRWh2VaY2Jxo8V2nCzpJFkMgBEgPsRkExGOpZuyVm3KkR7uGehkhCBB72rhPcbusXJv/r5+KESA4FiRd8UgNCW13GixNHlkOEO5SnLsCU8bUIPfOiviqhs+zvsiGmajYkjRzKnFKvYUY97T2yAIP1ZJr7K3H00ceYHV3U0rKtRakqLHxfBAMuad9ejm07OhfzByPbUwIKBp6vT4AEtTparUlDWfutbOg46RtPbDjoBWNYYb4wQh4vBgiveciNGKgL2uhhtWEAMg4FgqKfLRCGc6sFRpWbZ9z9N7R3sJDIAwwlBrSs22LIZDR4Yymz2/7nzKuqZGbrwo1xm8KSkL5UaPNbtfx3/2W2BbkcdWjRqsGEatpUiyEeFC+UyUJIkOYty6aTo36N55WoySUT4V43XTKtXaDsZ+BIFNhucuIIie4BnA3EogWCzWW7Iai/DZVAQ8kbvXm66Rf7bfTY4iieFcTAyzmmHWW4qsalslsLsIWhABoLasTy1VCAS5uMBsbNXfGp7iBSWjwqGBpGHZdxdLptmL++nuAoNnEsOAoFRtV+qSGGYODSZ3MGZWXNoyMSESZhttZb7Y8LM7oLgfe7kOOdv/AlXqUqUhURSVjgtCiPEOvKIeD1bhziZG/ihLRPlMIkIAarSVhqRZjqdh2FMVjq8X8Y/sAsYApuW492IIISousAAdMnkvYwOvKjMCYCgimxBohirV2uVq2+OjfRpnCLCD/PPvim4W620CoZFcjGM395XaEhgAR4VQPhk1LevObDGISbGPQJ7QAEg3rVJdrksaxzKZeHgn4eh8CQrn05G4yMuqWWkogHxB9kDiPqp5VjVKuS5VmwofovPpCEm4AXmxrzfspUuCTbvvnouApsgIz0bCIU03pxcqbsQ0V4jf5qZiG1i9rfLuJ2jLalPWACAmcvGI54Gzsp/Yun7Brj2oJzGSi4VDTK0pV5qKXyG0L+zgh3ABME2rLWstWWNpamQguUNqcKsm8EwmIVi2M1dsmD0dWtkDYACMmm2t1lZsB0f4UCzC7XCFxwAY8EA6GhX5tmIU6xJGByJWwEa4b9SwpkkqTaXeUiI8O5ZPuRqGDh3OluyA1n92XxA5NhMPm7Yzu1yzLHsf+gEF+whfJMIYF0oNRTfEMJeIhhmawitEBj1xnyeBBDYrBIDG8kmBY6otpdyQV4sU+3Cg2ateU9IKlbZjO/EIJ4ZD683+24FX5kiYG0hHLRvPl1qGtaODvDssTKnelmRN5EPZVISht75kbLPkfGLPJSMxkWtJ6mKpbttOf0OxCsHA7bTDFCqtckMKc8xwNgbB/ekrm/HNWnBNQAzkrbEYYxQTuaFs3HJgsdw2LQcgcBHeU+DOCY8xXiw3dcNMRPmYyK2QV6C932rI+QpbBIABOwgBgDOaS4Q5tlyXiq7/jH9z8y5GedukPO5/9bZSrLYZgsx7l8rfe5LuD4whInD5dNS27Ym5om7secDbrmVBCDDC84VqS1ISIpdLRnq1dW8MVzMdEUIxIYSxU2tJTUnrU8MKOgeuN00RAoBSrVVpyHyIHkwJyDviH0RG22L2+NbTYDbiQBcZFUODmahpw525km7a7lHBHjf4uwWMoVBXddNJRcOJCI/8zYy3SeghSBoC118LPO0tAADOp6IcS5Xr7VKtverhIPz7nlFgkENL1auSEmLJYyOZrh7EPQNj70Q94kN0KspRJCrVWk1JvQ97CrdzMCwWG01ZFzk2IbqBCHega/DlPookEgIfEzhVN+aL9YMRY6g77puFAlabfBqS2lY0gQuNDiQAYMVciDrk6C2BfeWlb4PmQnQ8ylumdWe2aBimG3YLejKz7gSoI7IRdhxneqmqalYqKiQi/NqrV7pYMLsmCf6BH/dhYjAtuhbyWlN25w9eHWVyL2UHxz31UG8phWqTYahjw2mKIu95nHvrBQKEgCIJkQ+lYwJGUG60NWPPjxh2LREAqrY0WbNiEW4gJXgH+u89NV8uAkjHhUxcVDRreqmy70rWbeA+O0q7K1tT0uptFWNIRPhUTHR9R7DrO9OTdBwsvJ7lA/yQhZEwN5CM2o61XGub/tYu6Kg9qZFXDASesRQ52JlcKCi6ERNCEd6NLOh0BItFK+9tlObKfUqBdQclY+FUTCBJsiVrzbYC67hgDxckTCCEMKBaU14q1WmCGkgJJHHvVIS8+2S9bSQfYg4NJAlAc8WmrBm7WfJe4I4PBIvlVlvRElE+n4ntjGY9rS0AIAyJKJ+IC7JmzSxV+1LDRvCig80WavWWKvJsJiGQJOGZjzqUeVsp3j0XoyC8TvB9NBwaSkcpiqi1FEnVLXu1GXAP4JYX+aFgXcF+udI2TDMV5eMijz3lCO4QXrbaMWHonDmu8EASxFAmHhP5pqQtVVqBQR46st4beB4iCHBb1moNhaXJkXyC2pEO0vf/wIAw4lh6JBsnMJperK5c3ID3tlYB3LNhumEtlpttVRfDoWRUAP+Gu3tO1Yu/j1A8wicivGaY7hGy3Sr2ruP+UQPGgWZnoVRvSmqEDyVjwtpJEgz4ewJFkiLPJCIhy7KK1ZaqGx2Da097JdBBOqpm1RoqODiTEBOxMPJ2Umse3rQwK6aMFe5DAOl4OMKHmpK2UGqset97bK8q6OqHTMtuy7qkGWGePZRPUb2FwNoQgY8LoBBDD6QjCKGlSlPVjX2Wul2Pk1pLaqs6RRAxgYvwoZ1vQpHvpJOKCemYoBtWqS4fkIDGXbHv1LDSFivuTIVqW1L1qBDKJoWOP0PHmLj3fmEZaiAZIQAtl9uq7mm88d66oAdSADYtZ7naVg0rzLFRkWMZcpVx1fvUg2PDyksrokY6GhZ5piWri57X7YqXBMJbR7C/V/jqobZakxRAKCbyYji0G6oNx5UTuRA9lI05gApVSdUMzzoQbBb31jqLAbDjGZWMVIxPxwSa2kYspg2w0jjJKJ+KC7phLRRr981xowfcF6lhzQjHS+VWS9ZjET6finRoewIT/o7yCofYQ/kMgYiFUktWDV8bhPcq8CbuuLAMgWFac4Wm5dipWDgcoj17xNptTW8lQWuoEg1lYokI31L0QtW7QhZ7J7Bwh3ixy8DguOlWmnKjrXEsnYmH/T3gjhIOEggxdD4dBYRmlyqSouOVAeFd3rCXemQEgBzHubtQVTQjFRMT0bDfaTvxa/DrgEHgmLjAkQjVmkpTUu2dBWHfO+w7NXQo5P2NFl4sNZqyHhVC6eB2E/fPu7E4hBh6MB3FiJherkqq5lPPnqnvUYfcg11qaNiOnU2KQjiEEOEZXFBgwkC9899qiQMNpKOxSLghaQvFhnvMMTjyiDqcrnYVKzv+SkOpt9QIHxrNJ/COHTFdu7Jr2WEZKhMXKcDVhtSQVMO0vZGAO+Pc9SRt3ROQg/HUUk3XrZgQEt2bCjocUu8lxQ6VGUkSkTCbiAqmg5arLcvuU8MK8Mo/DIblVBuSphlRIZSOi510sBsyKmIYKhMPY8BL5YaiGb6Fbw8vaO/UDJiWPVco25adS0ZEnvM9XwJHjHtPHAASEU7gaEXVi9W2opqugtILnbFXQhFCyJOuS7V2rSEJHD2UjXeGk7gnYISQbyDEFElExVAmHiYoutbSZNXoODzqPb/TemxWFsAYStWWYVq5RDgV5THe4VkH91ZQ77oejCEq8oOZqGVZkwtV/T4cIesJ++7ytPqDg3GlobRVg6aIZDQcE3nkLXyu0LALI4APMWODSQJBodJUNQutP0C7BwiOnpuWXag2LBtnEmLnnWgYVrw2e0uwY5vtBW/AYY5NiKFwiNJMu1SXHC96veu7sXc6SI/VKg2p3lJYhk5EuB03qCc/BZYdhiKOHcoyDFWotpt+pHx3N7HzTeYWQIAxnluuqro5kIxmEqLHtzvJtGPQIYSi4dBASrAs+9ZM0bg/jhtb475IDb6ZFyMH45lCVdaMeISPR8Ju3I410Wh3iBBD5dMxhqLKdakt67btaxv2avIg8N0qAEA37enluuXAQDLqOzV4lobVetatEu0WfIEgUCYeycRF1TDnS+6d4CvuD3taPQRQbco1SeO50HAmvnMZrNN7HmNMksRQOkqTxHKlUW91RLLae7EBO1jVjdliQzWdWESIhjk3v50QA7jSgp+GwLPZhGDb9nypZdp9qQEAfH8dXx5AGOPZpZqmm8lIOL4S9CY4XLULggNFopgQioY503EakqK4Roo9tFD4UxcDwkjTrZnFqo2ddDwc5uiOzdTa53sAXid1QSzCx6OirJp3F0oYo07Tyx5umQBZtlNpKi1ZF3g2n47tMLnVIZEQQkCR5EguTlNkraVIir4uf4A9YwfLccpNSdZMmqJiIsdz9M79RFz9T3D2JBJms4mIZTvzhYZ5346QbYFdo4ZtDER/2rvy9GKpqRtWOi4kouH1D+1cbkAIsQw1lInTFFlpym3ZC3yyR5tx3PGfZTuyYrQVnaZQIsKH2ODGnV3LOi5wCZHXDGu+WFud7J6a96Ala21FRwgiYTYqhHx3rHsG8uQG/3JtmiKPj2YYiirV5JbcJVZNb414LyuAYdmLpaZjO/mUEI9wnivXrg4WgWPS8bBhO3cXKqpmbnv525ewsbsoNfRoSPfiA7md5jh4vlDXdWPV5eurbHQ738UiikTDAzGWIpdKzVpLBs9pZ08mjxsfyHWHVDWjWG8BQQ6kohGBo0hyW/aILmmvc/TIJMLZpKAZVqHWAux02jD29FrEcl1RNVPkmVSMp8gezf4bPoN85WqgIKYpcnwwyVBkodKstxXvCC7exgqE77UFdMOcnCtblj2YikT4lUuJdtKaK/5cgAAQzzKJCA/g1JvtpqQE3g2+VNEDV+x9DJidUkMQ7wz87eJW9cK+H6SraXTuLlQU3UxG+ZgY6jnHYEe9NRBgkiByKYGmiHLDDaYYOBf08vr2p7LnnIPbsja7VCMRDKZjIbqn00dBfNced1KpuJCJC6qmTy1UHU+LsY3GuQe4yvr5Yq0hKVExlIkL3vc95Ng5WtYBBSZdBEAQRDYVoylUa8tNSbMsB7xeD8SybUgEm+a7Frph3V2ourf78iF6RfHa7e0e0wy8GtyxR1FkRAxnEyICXK5L2uqz58gXoe45u65PbndvvlNq6IiEvfLNFm8AACCMEQasm9ZytaWbdjLCx8WtA+yuRi/9jQGAJskjgymapuqSJmsmgBf6dDsZ9d6sKwubaljFukwAzsYEht7iZtdtDd8AIs9FBc4wzaVyu62YzkoQiL1Sp7i1mCvWmpIqcO7qt731fMMR0nE+nSCQGA65q0Vd0pqyDuASR2e1tujBgNM3j6O9phCmZS9VZQs7g9mYGA650jvaYMfkjv/Ne63D9BkkgsIcc3go7TmDdxwh8yNTo66jrkfFfNeYHdtV6u/ChsJv954eDi6qRghbll2uy4phhFgyGRdFfmupAQfHdwOvw62YCAAokjg8lKYpcrncbLYV/yDWNlad3tnBXdncQNiqYZTqEiaI4Vw8xDKbD2UUSNXgWWd6oQkuRMVFXuBDpmMXq23LCtTgexaPHGGModqQFdWMCeFMIoKxe/vP1k20SaxP1zPCn0QYMCYQzmfiXIipNKRyve1rHpH3cE9y0ary9Ei7hmkvFOu2g4cHElGR98gQb5hfV1Nap7EZ+dEavEjigBHgEE1lEyJgWCg2gtOlyOOazpp2rcIWnbs2JMo9YXd0DRjjYrHUaNS3fNK37CHAyDDtuULDspxMIhIRQmuvSO36OkIAIMtSuVwyjF4iKWMMmCBQNiHQFFmpt1uS+1avU900zXq9Xq/XLatn+7Pv2iLL2kKxDoBzSZHtLdqyrmvlckmWJeiN5gmEYhFuKB23bXtmuWKYrmi6h7oG162iVGvLqpGMCoOpGLitvFXgCU3TSqWiqiob3FLj/vTmA0IIYZRPRXiWbraUWlN2hXHsyhb+lm3DQmLcbNTr9ZphGME3PR3vx6Dp5lKxbjs4ExMEjvEFj+5zzP3SMIxqtdJsNjqqs8rYvCpjhDACjqWHMjGMiMVKS9HNVXVZaclVpOOL57jVbi8uLmxZF/Bp694E0t2hBoTQ5cuXb9263cOU811eARu2s1BpYBvnEqLY4Q60JRYXFz/88EP3pratiwaIJIlcKhIOsZputRVNN01X4OglL1VVb926devWLU3rKaY7CvSsAKphlesSgdBQJhpit6YGjHGtVrty5crS0lIvebkQeTabEC0T35kt6abZI+XtAMhxnEK1LWl6RAilY2H/suIt2rNWq7377ruVSsXeypLvi3RoOBPjQ0xT1pqSCr6sh1aiV2wIy7ImJu7cunWr1Wptq26mZTcltaVoIYZKRMIhhsKAXYtwV9HA/bLZbF6/fn16enqTlN2IZoHyimfpQ/kkIDRfbCjqyulSd2R2V8b426L5+fnXXnt984qUSqX5+flqtaqq6nb2UyvYhdurXNy5czvQsG4ySlY0SQgMy5ovNRwMA6lY77sJjHG1Wp2cnHzqqad6KxoiCBTm6ExSmFok3VsMB3o2xRuGMTc3537o8RUAQAAOBlk1Kg2JJIlD+V6jLbfb7cnJycOHDweV3bxHMQDPsem4YNl4ernuG8n3Un2NHVk16m3Vsh2RZyJCrweW2+32rVu3nnnmGWeTA0V4RU+CAEYG4mGOrTTkUk0CT4zGHavZhtk6jjM/P28YhqIoGz3TFYpmLFWbNsZj2XgkHCIJopdVxL1YdE29uvRd4MoKOMRQuYRIILxYrLun/oI9gGc9Q10TwQBQKpWuXbu6eZFeeeWVmZmZ0dHRkZGRkZERhmFYlmVZlqbpXsRz2MU7LxVF6WldxSvxVnTdmpwrm7Y9mIlGhC2oIWgjhJBpmqqq2rbdu5SIEAwkIxzLVJtKuSHlU7Eep4/jOG69NhvQqzJDbiVlTa80ZFk3EhE+EeEpauv+wBjbtq0oimmaQWW3qiOKCdxgNmY79nK5ZVodvNxxFGkXgTFerrQUzRR4Ji5ybqhlBM6W88eyLEVRLMvqLpmDb/xwL5ZEAG78yxA9vdgquVGze46IizHWNM0wjEBC6YVnAaAt67PLdYTQWC4eYijwNYfuLiZ4eY23rm3bqqrq+opr1pq8AqIH/woFlqazCZEgcK2tSIpmWTbt3iS8co07Bs9Rau21l4ZhSJK0eUXeeOONX/ziF9lsNpfLDQ8PuwQxPj6ez+d5nidJkiAIiqI2aZAdUcN6d+Ytj9n4dyVgAGSY1vR82bScXEIQOwzI3V9cE/wEd5fx1pfRf4wYTMW5ENuS9aake1ca7sXi6pO/pBi1tkqRRC4ZIQmiU4u24avdqrNVe0JMDA1lIqbl3Jmv6qanEFk9kncTDoa7i2VVN1ORcEzkgjgKW953v6Xnuz8fVjCYifEhpq0Y7i0eCHynkRXF3mZYo4TbIPdVDCprxnK5jRDKJcIs7QWn8aNyrtRwPdFsnpdP9ATGXoY0RSRifComFGtypS5LihaL8CgYkyvKolWN1qmr3rTq0Gg0bt++ffv2bYIgWJYdHh4eHBw8dOjQyMjI4OBgPp8fHh4+dOgQz/MbCRHUpUuXbt68uXk2vWB6ekrTtL/7u7/bnJsxxr6zESo2jeVq23Hsjy6/5ZRvhntWN1y6dGlycvInP/nJ7du3t3w4GLV3Pi5rant63vnJL16eufpmjxOnWq1+9NFHAPDd7343Ho/38oq7aWqq6MpUGzuW1ir94z9+JxzqSdcwNTU1OTn5yiuvtNvtLZ93oenGx/Mt28EL5db3f/jjXJQE954u/xTWRt2BMb569Wq1Wv3bv/1b6FlRZzvOe9Nyrd4MEealt9/A5ZuAXB8VYnO1+eTk5Ozs7M9+9rOJiQmG2WIlCEpYXFrQNO3a9dt/+w8StjQEDgABfuzdjYqr6/qVK1cMw2AY5sqVKxsljnwXgmBOLjbM63ea2LFnJq7/8Ae1hMB2bHBWkV9nc83Nzd24caNUKrktCV0bE6+EnnXl5qZiEoYMGL/y1nvS8o0oT65Lv3sV33zzzXK5HOTVFVNTU+4HV+ydnJy8e/fu66+/zvN8NpsdHx8/ceLE008//cgjjwwMDLBsl6lHzczMvPPOO71Ky+sQ6D9d9dJbb7211Qte61i2U5ShKWdYmiwuztnVqfWLxkZ5TU1NFYvFa9euFYvFngsKVY21TW6hoF1SFhtxHfk3SW4OSZLm5+cB4P333+d5fut8/EKWFWKywRLAEqby/uVLFNGTdrBUKpVKpdu3b7vS6ZYmTATgYFwz2LiQqsvG62+9lwljhgRf3dvpeNLFSL6wsNBut91e69FcamN4fwkkPSJGiNLi3NvlO245ECY2v0yoUChUKpXr169XKhWSJANjxObZWaoYoum7c4s/bt1JcJ1y/WYxni3Lmp2dtW2bYRhXVbS+dqukdD+pgkzcLDAYcbba+PhqkSYwBH4JCLqOGIRQpVJZWloKWrJ7dp4Eu1JowyE4OkYiuH77rlY04iGPC7Zsk8nJyc68uqJcLnf+6k5wQRASiUQikWBZVtf1+fn58fHxdDrdnRo+9alPnThx4p6Nn0ETzM3NHTp06N/8m3+z1QseTbcU/d0bi+98+1IyJjz/u587PpzoPa8XX3zxrbfe+vrXv37mzJneiokxgvmy/P/5x8t3F6sPnTv9J79+bkvx3kWxWPz+978PAL/zO7+TTqd7yw4A4PWrc5WXbxpN7de/cPYLj4yEmJ5CJ169evV73/veM88889xzz0Fv1IAB7i41mz/6qHln6dEnP/P0+UOpaHjNrNmIGv7yL/9yaWnp3/27f9dLXi40w1r4m5crM40LDx/7zYuHh9KCX44VUbgrPvzwQ1mWv/a1r505c4Zl2R6p4Vsv3f7JpbuxMPPZZ4596sywA4jwVvjNqEFV1X/4h38wDOPzn//80aNHu9ZuPTU4GL/20eylb77FUNSf/P43RtJhiiT8twLBoQvu3Lnz4x//OJ/PP//8852J+3/HAIAwwsjflwACAFkzfnxp7ju/+jiXz3zpmROPHs8DwgiILdvkRz/6Ub1ed3ttIywtLd25c4eiKJ7nRVEURTEejw8ODh45cuTIkSOjo6MDAwM8zyeTyVCou5qPyufz+XweepYnN0IsFstms2fPnt38MezfF1usSXdKDkIonYicPH7socMDsIH45L3YUbw7d+7cunXryJEjW2bnZ+kAoMGmnP7VxK3ZSkiInTp9miJRL7bb+fn5bDYLACdOnBgcHNw6Oy+kALpddix0l+fRE4+cevjsIZbZ+mY0jLGiKIlEYnR0NKja1v2CgYmU8u/MfjSxjNnI6KEj40Mpf6au2hKvTyqTyaiq2lMz+pA1wyHfdaA5Mph9+KGTg5mYK4/DVtWTJCkajY6Pjz/00EMcx/VYu+vL5nuTZYwhnhk8e/asjYHwFNmbaRtkWc7lcrquHzt2rIf1w1skVN24vmzaBBUJsY+cOTmYiREdV3Jhv8Rd9YvpdHpwcLBrS7r+GAgDEAGbIQCQFW2mjn/42m3NoVK5wTNnHwJPJupetaCtrly5wvP85r126NCh8fHxRCIxODg4MjIyOjp67NixdDodi8VisVgkEuF5fvPGpzo1/5vktAncFEiSJHuNKYwAQFGNpXKDQCibiNA0tS2V2ZbK1XVFRAihqMBFwiwG3JK1tqzHI736ZfdcLy8zQAhj3GwrlUY7Hg2P5hK9X/rmtuR2+yLEUgPpKEJovtSSV3vdttttTdNcfy2apnmeD4fDG6e0BTDGumGVG5Lt4FRCiEW44IaxLUt8b1XLJCIRgVso1guVFgAiVg7sb5GOOyB7y87TRLYktVxvI4SyySgXotHqXgs0kOvfd6u2kT7PO0u4hsswUCQ5nI5SFFGsSy1JRYE/DGAAYhOZ1h3/m1fpySefHBoaGh0dTaVSiUQimUxmMpmuG4eNQPVo1OmKTgtFMpmMRCK9vQYAoJtmrSkjgIGEyDLUlj3dKf5xHBePx1mW7aXkgdKXJslkTBB4VtaMSkMJbqzeHCRJuvXqkSDc/jdNqyVpbVnLJSO5hODerbH1uxizLJtIJDiO69GvAQAAAR+ixweTCEGp3tYM03W1dTCWZfmVV165detWvV4nCCKXy509e/bixYs0fY9XWhuWvVSqyarOs0w8wvOu5hgHhxs2KyrLsqlUKhTy3F6DwbN5HZNRXuTptqIVay2AVRIQbLyeIYQikYiu69uqaa2lFKothiZHsjGS9JSdm7e+WwCapmOxmCiKGz8Y3OPqlx+AosjDI9kQSy2XWm3FcDAmOgXndbkHlQ2HhUwmu3ldnnnmGYIgUqnUGhLpbO3NhxYFqy0x26KJzn567LHHXMF7i1fcHRdgVTPLDRkBGs7GQgzViy0qKOfg4OD58+fj8Xhvk8fXjWE0kIrGInxTUhdK9aMjqR6qCDzPnzx5EgACGXgrIAS42VYbbQ0hMhHlRZ4FcLZUbbgVSSQSjzzyyODgYM+UjQGAZ5nxfAIQmlmuyaprXcetVuvNN9/8q7/6K5qmBUGwLOvKlSsffPABy7IXLlwIRoxrdeux9w3Tni3WbdtORUWepQEwcq8ZWtn4b/h6IpF44oknUqkUQRC9D9B0XIiGWVnRijXZPzJLbEmzFEUdP37cNM1Nl6uVyeeachqSXmrILEWOZeMEgXyFp7dD9JQN65oIYxyNRh966KH1BqyAvzxTiGuew16tSZLIpqLRcGjOajQkTVKNCB8K9igrhsp1OY6MjDzzzDObt8DAwMBGtvAe5zgVvND5YbtyBELo7NmzPUmq/q2ukmoslJoEQgOpSI/nC4LiZbNZdzHvpZwIEMbeob1kLCzwTEvWlsrNHnMMhUKHDx8GgB6FMQQIY1xuSrW2wnNMPh31vt7yRYQwxpFI5PTp066+s/cuYBkqkxAREMWaVG+ppu2QCObm5v72b/+2Uqn88R//8blz5zRNe+WVV1566aX/83/+z8mTJyORSLCRDIbLljmall2sKY6D8uloNMz5t3O7U2yLd2Ox2MMPPxyPxwmC6L1qiSgfCXOGaVfqUkPW42EavANImyVBkuTY2JjjOIIgQIdGYGUxc4+xdZQZIdSUtEpdZhn6yHCKIonAWumZ25H3WPBK0GiiKB49enSNrLeB11PgvoEBEAGQjoksW623lGpTEnkWAUZAgBfRf+1O300kn88//vjjmzRakLVruWy1Wm4hXZENY6yqqmsdF0WRZdmuPdJ9Tt7D/oIgNtxrrU0bABDWTbPaUoAgB5Iiw5DbijKAECIIspehDL7LEwaMME5GeJEPFcqtWkvt0UIBAIQfsbKXh13JsdHWWooeDtEDyYi3SGx+fM+vl5vddtofAQBFEjGRj0e4SlNyI6YxBJ6anr58+fK//tf/+ktf+tLAwADGOBwO12q1l156aXl5meO4TueCHpcEN5aBbePBbCwSDgFAcAch2kr4RggRBIHQym6il+qxFBUTOIFjVdMsVNsxPomQL6JsmkJnr3XXpuEVA4lrT6i3pOVKk6GpsYE4RRDeAU8IdBFdatRZtaDjumSHPbGjMx13EzaQioVYqt5W6k1lLJ/wzCV4xatrvUxHEGjz7W2QteM41Wr1Rz/6kaZpjz766JkzZ2Kx2PLy8uXLl6empnK53Gc+85lcLte1L3YxyhPqLfIMBgDLdtqKVm1IBIGGsrEQQwaeIBu+tsqi45JCL9l5jyGMMEKD6VhSDLdlbblS7+HdtYn0+ixGlYbcaCnhEJNPR93LFXo0D/dcrzVvAUuTR4ZTDE3VmnJb1euN+uTEhCzLTz31VCaT4TiO5/nR0dFTp06Vy+WNToutGyKd5jcMALppzSxVLcdJRLlQiPZEBjci5bpSd6uyWztPTumlagRCqVg4FQ/rhlmqNh33Xq7VPoKbJLVGNxG84QkDCAVCE8ZOva1UGjJDkYPZKEkQgLx7MVaUg5thpeO6lMdTIgSF9j8j1+OTrjblUl1yCwQdl7d23XltVN31+ZIkaRjGa6+99td//dff/OY37969WygUfvnLX/7lX/7lD3/4w+XlZehQoq15ffeoYTsRqVTdbLQ1y7J5luRDNEkQsPWNt6sG0yYe2d0HCkKAIB0TIuFQW9GWK60tnbzcTbib1/bcPhCUaq1KQ+ZYOpcQgvJv4/3e2QG7IwWTJDmSjbIUWapJTUltNBqzs7MEQZw6dSowXMfj8UOHDum6fvv27R4Pkq4uFZheLANnIBkVOdZvoS51W+9nFey7veR6bBAEqWg4ExNUzZhZqDrYDRoTyOQbJrU6665CSiDmIISQopvNtqbphsDR+UyMJAm3XoFgv6VMtGleGyaQT4l8iKm25ErTDU3YWfJe5GLYJF93H/Hwww+XSqVf/vKXb7/99osvvvjDH/5wZmbmxIkTn/70pxOJxEY9spsRpW3HMU3TNM0tn2wrRrWl0TQ1nI2RJOkReA9ZYIx1XZdlWZZlSZJN0+xt8XGfwTGRFXnGtO1aW5PVLU5SIoQcx1FVTZYlWZYMw+jJZxRjAKi1taascSE6lxABVhaNHt7GlmVudAapWym9hY0i0XAmSpNEqS63JF3X9Xa7TRBEPB4PlgWWZUVRdByn0WhseTIa/HIHHzDGmmEulOuA8WAmKoZZ9y9oIz/BdZWzLNM0jS3X3zWIRfhEJKxp1nyx4WDvFvJN8nMcR1VVWZYlSdI0zbbt7go5t0z+lqLaUGotlaHpTELkuQ2v8FyfsWVZbl7uCcPteg8OZ6J8iGkpekNS8eoG3wQYg2mauq4HYzLYdKwpZzQa/c3f/M0jR45UKpXvf//7f//3f3/79u3z58//2Z/92blz5zZx8N2dQ9kYYwy40WhYlkFRlKu32+TxRlst1yWGIofSMZIgAKPNPVjAX8Ndt+WbN2+VSuVcLnf27EODg4OuHiV4ckMdLAaWoWIRPsyFFN0sVpsCn95kBFiWValUbt++fffuXXfGjo2NRSKRLayYCNsY1VtqWzFEITQ8kPDy7uE0l2VZ7XZ7cXGRIIhkMtHjQQO30WiKPD6apWmqUGs3JDXX4eHWdTHZMtH1ujTDsptttSnrYZZORniOob2qeZb7VWmu2W9bliVJUrFYIAgUiYjb00RGwom4oJtWsdZGgT6wI8vO3bht281m03WKsyzr1KlTx44di8fjq214q7SPbh2KtValKfEck0tF0aqDlr44ANDp74T9IC7Ly8vXr19fXFwSBEGWpfHxcdcs0mMFR3OJMMdMzCnlhgyBYOUZgzFA98Gsaer09LRhGOPj453Te73OiGXZI0eO/OZv/ubS0tK7774rCMJjjz32R3/0RxcuXNi8YPdODZ1DByGkyPIbb7wxNT05NDT0n/7Tf9r4PQQYJFWvt2WKJnNJkSC6DKyuqNfrP//5zy9durS0tKSqOkVRw8ODv/Vbv/Xoo49Go9GuBevI1PsyJvLJaFjXjYVSY3wovVH3qar6/vvvv/zyy3fu3NF13TCMy5cvX7hw4ZlnnnEdbzepYEtWa03Jtq24yCdjQlCEzWGa5uLi4ne/+92rV68+99xz6XQqk8n0oK7zVHIUSY0PZRmGWqo06205F1oZwWsSIQiCYZgtB+7K3PZpTdOtckMBIFJxMczRJIF82R422VO4VZuenn755Zfffffdo0ePjoyMbMv3JhUTsglRMcypxRoEzsb+mOmsna7rN2/efPHFF69du+b22jvvvHPu3LnPfOYz586dW1OqzpIiQJWm3JBUPsQMpKL+TqjjgKfLFWgVp8iy/NZbb/3qV7+an59XFBUhlEoln3zyyd///d/vmdYhFRc5hmzLarUhKZrBh2gAgHU6yE4YhjExMfmd73xb1/X//J//8+joaFCkNR+C+uZyOYZhNE1LJBJnzpxx3fA3aA0P904Na6bf5OTkP/3ony5devfRRx/dlBowIGjLWr0pMzQ5ko+TBOl9v5Ua0jW8kSQ5MjKSTjOS1H7hhReKxeJ//I//8eGHH+50pFlrNwLw7MkIxSNcIsLVmkqhJuGNM/3444//7u/+7sqVKydOnBgbG+uM9ZRMJhOJTU58oEK5JSmqyDMJkSe8IbzFPGy1WteuXfvVr371yiuvfPTRR6lU6jOf+Uwmk+nRBAN+JCuahOWWVG8q5EA8Ho/Ztl0ul4eGhtw1U9O0wPepR18g3LERkhR9oVQnERzKJ0Ms4++SvFp39mCnKVTTtA8++OCVV155/fXXr1+/vrCw8Ed/9Ee9ZB0gJoTiIqcb1kKlKal6jGIJRHSUbiXHu3fvfvvb337hhRdOnz49PDxsmubU1NR3v/vdcrmcz+czmQx0X8wxxlBtKo22KvLMaC4OsIrrMO4i8um6PjEx8Rd/8Rf1ev3EiRPpdKbRaNy5c+fKlSvHjh27cOHCRmcT1oChybjIcyFaUc1qUw5zsVUSyxqbK8YIoXK5/PLLL//gB98zTfPP/uzPxsbGNklfVdUPP/zw//7f/6vrOs/zlmW1Wi1Jklx23mSA7WhDEaS7uLj43qVLjUYjHo9vFUMRAYZ6Sy5UmwxJDCRFkkC9CNsY40uXLomi+Bu/8Rtnz55VFI0gCI4LvfDCC7dv3z569Khrwe5qpvKUSAgQQDLCp2LCYrk5V6htsiu8ceNGrVZ7+umn/+AP/sC2bcfBU1N3/8f/+B/vvPPO448/volVGQMUapKkmZFwKBnl3U34ltUrlUovvfTS9PT0E088MTs76zjO+tV+cxAIxcVQIsLPFRu1lspwIydOnnQc5913300kEq6IWygUrl69yrLs6dOne/Hgwq7Rzh+WLVmZXqySCEYH4hxLw2pu8E19a9u/Uqm8/fbbi4uL4+PjpVJpG2oUN1UAiiJFjhU41rKdQq0V5hIsjdaoydwpNDU1NT8/f/78+T//8z93M1pcXPzmN7/5zjvvPPvss8FS2VlBhBBgjAAVq+1aUx7JxUcHEitUEAyddZE2ZVmenp4uFAp/+Id/+MQTT2AMmqZdvfrRX/zFX3z/+98/ceJEj9SAEAxl4omI0FL05UpzxCWm1VXr/Fyv1z/++OPr1z/O5/PuVneTxBVFuXbt2l/91V9dvXr18ccfd7daV69efeutt37jN34DVksNa8bbLugadF3/xS9+sTA/Pzw0HI2KWwdKQyCpRr2thTlmNBcje9OEIoROnDhx/vz5xx9/PBwWGo2mIIQvXrz4gx/8oFaraZrmUgNsICP5AgKOhEMxgVM0c2apskmzDgwMuIf2jhw5Ui5XAFA2m/nWt75VrVbr9U0NnxgvlpotWYsK3h0NvYRUIUnSNTJLkvSzn/1sO7yAAhs/RRKjA8k789VaU7EQc+zY8Uwm8+KLLx4+fNj1//nwww8vX7589OjRY8eObTlwAxVCAEU3CzUJEcRwNsYyVPCcH5Wou57VsqxDhw6dOHFC1/Vr164F0kSPcJkmKnJDmVi5Ic0u14ezcZZeqyxwkUqlPvWpT+Xz+ePHjxeLRYxxNpt1Q6G5h5RXtWqHHcB2cLku1dvqyfHcUCYaKCBWl2MVCIJIJpNf//rXf/3Xfz0Wi1WrNZqmDUMXRXFmZmYbQYYBp6JChOeabWWuUHviodGgQdc+h7Hr0nrp0qVIJHr8+LGZmZlN0pVl+fr169/73vdeeeWV06dP/+Ef/mGtVvvmN79548aNn/zkJ88884woimt4p/P1nVKDZVm3b99+9dVXY/F4OpW6cfPjUqm0+Su27TQlrSGpiVj40GCaJMkOq/GGgwYh9LnPfY7jOEEQqtWaJEmaptZqtWg0GolEAvF4U9MRBoC4yCeivGFahZrsbEwN586dO3nypCiKNO0uj7jVkizLEkUx4KCNyrlcbrRlfXQgkYoLvmC6xXYpnU5/7nOfGxgY+PDDD7c8ObMGHTdxoXwqyrN0ud6utpSR4eHPfe5zb7/99gsvvHDs2DHDMN5///12u/1bv/VbsVisxwCBnd43imYsV1uIIEay8ZCrg8SwEgVlg2ZPJpNPPfVUKBS6efNmz5muLYPIs5lkeLHSuDNbfvzUCHBddvIIoePHjw8MDAiC4CpTXL21YRjhcDgWi0Hn6A8ctQAAkKzoTVmzHOzLegCugipIfJV4hBFCPM+fOnVqaGhoZGSk0WgoioIxrtfrCKFgB9cj0nExEg7VWlKpLsHGAwUhtLCw8M4775RKpSeeeNww9M1Jdmlp6fXXX3/rrbcymczv/d7vPfXUU5Ik3b592w3rcvfu3YceemiTfeXaCpimubnFmyRJlmVdLb1t27Va7R//8R8RQmceOkMz1O07WweMkjWjJWuW5YRDNE2AIiub+DS44S4BACHkqltqtdrMzMzNmzfr9dqrr7766KOPHjt2bNMgKx4Jm6ZpGCZL4ihPGYaxXG03WhLPUMHyQBBEKBQiSRIAB+dBNE0HcJrN1q9+9UtN0x555JHNt3YAuNKUFd3kWZKjodVu+ZderGIHhBBN00EMT0EQBEHo6t+yJdx56bp75hIiz1K1tlxpSI8dP/ov/+W/lGX51q1bExMTjuNQFPXMM8987Wtf286hoxVtX0vS5kt1giAG0xEvONpWV11gjN1gAZ3fbNO8hxGAwLHpmGDazvRy1fCugevCtm6cEgBwTbOSJL311lvLy8vHjh07duzYupRXFCXFmtSSNTHM5pLRTrd9tAGpY4wZhkmlUqlUCgCmpqZu375dKBQnJyei0eiXv/zlXqL+BJkMZqKJCDdfqpUb8iZLiKqqr7766uzs7JEjR06dOnXt2tXNB0mr1dI07ezZsw899NAXv/jFZDIZjUafeeYZWZYpiioWiydPntwGNRQKBTceXGf/dZpMo9HosWPH3A5wQ8289NJLf/qnfzoyfGh2bsZ9fv3S3flNva20ZI1jmWiIvv7xx81m08aOGwNp/ZAZGxs7fvx45zfz8/Mvv/zSG2+8IUkSRVHf+MY3RkdHgxqu00Gu8H6hUJydnZVlubQ0b5lGudZ69c13RIYkEQaEMYAoiCdPnozFYr44iQDAcex2u/3SS7/66U9/evTo0c9+9rObnyLDGJYrLVnR1XZt+s41pTwDgAgMDvLa0W1GgiDcSJ6b7/m3o25AGOHRgYTAh5qyXm+rQlh49NFHKYqanJxsNBoEQQwMDJw4ceLIkSO9pImgQyIA0E2r3lYbbSXKhzIJgfbmT6BJXzukOzWRO69gVAgNZ+KO7SyXG9bKPTwbymIYY8Mw3nrrrZ/97GeCIHzlK19ZG2vDUyJ4VsL5Yr0la3GRzyUjq3Wr3TNYU+Zf/OIX77zzTqPRoGn6ySeffOKJJ7ZlgsmlhJjIt2W9UG0Gp6s6M3a/++ijj1599dVsNvvcc5+V5Q0jZQdNmsvlPv/5z7MsOzQ05Lo2kST5+OOPDw8P67ouCMLmog2FV+shZFleWFgIfu1sCMdxCILQNM1dvW3bnp+f/4d/+Ifjx49/6lOf0jQzoIbNDOkYF6utalMJc2wmzpdLpVK1Ytt2V2pACK0/zcaybDwez+fzbvdPTExUq9VUKhW4G6xmB28IYABJkgqFQrPZVKS2yDOWaV75eGIkFWYpBMjBGBLxuB/l3ZN7bdsulUovvPDCT37yk0OHDv32b/+2O9k2aVBZ1Yu1tmE5BLaVZn1BbgAQJAYbBb5BGPyz3m4QnU3Qo4XCu1YOwUg+IfChmUK9VGtjBAzDXLhw4bHHHlt5uvez3h0ZIMBtxai3NJoic8mIGOZdB1YvSdS9x7uuEGs+91AMhAFiAjeciVm2PTlf1g0LgX+nQ7eKOI7Tbrd//vOfv/DCC9Fo9Ktf/eqzzz7rWhPXLRsIADCCxVKjJSkix8TFLVb7rk2XSCTy+XwikXAcR5blmzdvPvLIIz0e1cUYJwRe5GhVN8oN2bBshqY6M3I/6Lr+3e9+17btJ5988vjxEx98cAW6GSk7v3TDw64pbSDpbDkGqE5eQAhlMhlX/Y7Webm7D4RCIVfdXSqV3njjjffee+/P//zPq9VqsVBeXFhstVqKoly/fj2ZTCaTSXcxX11JKNelWlPmWXo4lzp16vCYqmNwMHYAAK3zzkylUmvayDVGPPHEkxg7L7/88l//9V+Pjo6m0+l0Or2R5dLdL2ezWYqidF0n44WPSx/PLDX42MDD5w6LvHflKRdiRVEI6FpV1bt37/785z//wQ9+cPz48T/+4z8+f/785ooGB+NitWVYjiiETh4//OmLxwA5GAgCwFlnhkkmk27ICVjdx0Fle5vA7vLpBTjJxIQQQzXaSqne0nWTZajOpgsS344i0DPo11tKsdZiGebISJbqCH6E1jkXBL9utkKsFkU3Lw8CzIeYZJS3bWeu1G7JumVj/277tS8ahrGwsPDyyy9/85vfHB4efv755z/96U8Hbi+reMFXNwDgxXKrrZi5ZHQgsUnMhVUpdJb8+eeff/rpp2u12rVr1771rW81m83/+l//a6+n+BHiQ3QiynMhRlLNcl3OZ6L+OuLl6DpovPbaa0888UQoFLp7d3J2drZcLjuOc/fu3Ww2m0wmu557XjO71+xYu/Za8OvaBTAajfI8v2Y8BelCR4SZxcXF9957j6bpiYmJYrFYrdQXlxYXFhYkSfre977nilVr3MJcQakpa5Ki8yFmbDAzODSMHXfNw+AdR11VEzeak7sO3L17N5PJpFIphmEEQUilkrlc7n/+z/957dq1p556Kp1Odx/3fi2i0aggCI7jtBxu7OPi1GJDtemh4eHgrmeEgKa9uWTb9u3bt1944YV33333zJkzzz///NmzZ9dodNfDcfBsoaEbZjYhHh0bOnr0CHbP3AHC4LhHmAPCJUkyiFW1pue2pcYPlAGAiIgQikU4hiZlxay1lIFUZKXlNzZTdUnT4xoHY8J9sNqQlkpNhkL5pOAxQ0cCa1LrWqkg5TV5bVVTDAAMQ8ZEPhLmmrJRaciaYQocsV7Ydxxnbm7uJz/5yS9+8YtDhw59/etff+KJJ9y4HuuS9SKtucy6WG60FSMVE/OZ6Lonu5XJd8y1bfv48eMMw4RCoeHhYY7j3nnnnRdffFFV1V5FM4wRQqmEmE2ImmZOL9dyqQi5OlScpmkvvviiruvFYvHVV1/VNG1hYWlhYc627RdffBFj/OSTTx46dAjWzdmV2nYT4jbhBeikBvcPnXHcNsrGBcdx4+PjJEmGQiHbti3Lcu+MceX8zqtB1qRQqkv1ljKQiQ7n4jTDdGyrNtw62rbdaDT+1//6X6dPn/785z8vihGECDe8l2vRCTzJN6o/xjioWiIi5JKijWG5KhEEGQqxrhovWHsBYHFx8aWXXrpx48Zjjz128eLF4eHhTSL2B3AcPLFQUXRjfDCZTkTYUKijg91LXLpHzekkNeyjN3bwDxECAABBoMFUNCHybdUoVNtutIj1a/iWKXtakZUncVPWK02FpcmRXIwgVoUn2yitoFLr9Vadv25VUwSACYSEcOhQPnV1cnG53FA1Q+A842vn6+Vy+Y033nj99dfPnj376U9/enR0VBCE9ePZg2fOBt1ylsp1RdOjwop5Ysv2KZfLP/3pT2dmZv79v//3yWTSHWA0TTuOYxhG71s2d72MhUMJkas2lbnl2pMPjfr+JCurSDabvXjxoitmmqZl27Y75oN5B6u5eHORrWsx1nyz2bZ5zcBdg6Ghoa9//euyLLu/Tk/NXr9xXVXlSqXy27/929lsluO49SlgB5drUq0tHx5OZuKCt0XGm2h8APyd+fz8/PT0NE3TJ06c1HWtXq9+9NFHJEkeOnQoUElsUP+VOY8BIuFQPh2zHWe51vbV3bAm3MCbb775q1/9iqbpo0ePYozn5uY0TaNpmmGYWCyWTCa7ltPBeKHY0A0zGeXjQihY0MG3+XflBcuyms2ma/SdmZlxfRanpqYsy2JZdnx8fKNmWVVDrwVxJiHEBN41kj9yYgh6mn7d4Y1ODK6sV2m2Qwx1dCTrCvPrNY9de7BYLLbbbdM0Z2dnFUUhSXJycrLZbLqBz8PhcI8FCzHUUCZ6bXJxeqnSVvR0vMszH3300U9/+tNCofBbv/VbJEkuLS3pus5xHEVRoijmcjmvoNgfcBgcjKt1uSlrDIkSkZAY7slPCWNMEISu6y+++OLRo0cfeeQR15Fhbm5uenr6woUL21JDIoCoEIqL3GKpuVhqYP9gaeDewLLsr/3ar128eNH1hatWa9evX//oI+7DDz987rnnnnzyyc5Y5/fc3WvQhRo2SnfN99FoNBqNBkQV5kXDNGZmphiGefTRRzfKT9XNelvRDNM1RwVpd1Nyr4AgiEgk8uyzz/70pz/9+c9/fvXqVYIgTNO8e/fuyZMnL1y4sCYMfLcqrPwaCYcG0zHHsWeXK5ph4hVHN+SXBa5duzY9PR2LxV5++WVd1xFC4XCYJMlEIvHUU0998Ytf7FpOjPFypWkYdjomJFZiT/oXH21w0ZwkSe+///4LL7wAAOVyWVGUiYmJb3/726IoptPp//Jf/stGjdlRL+x5gwPKJsSYGKo0lcVKc+WhexkoK684GKpNqVBtDaQiYwMJitxKzHP/ijFC6K233vrggw9arVapVGo2mxRF/f3f/z3HcadOnXr66afd4Hq9gGWogVQEAZovt2XV7Jr53bt3b9y4QZLkG2+8oes6xpjneTf+3blz577xjW/Ayo7Gi+7rYDxXrGuGlYjyyWiYoXqKAIoQSqVSTz75pLt5mZycZBhGVdVisUiS5O/93u9tGidyPXA8Gk7EBNWw5ooNP87dylpFUVRgfMUYFwpF07QkqZ1Kpc6ePXvkyJHt5NUrulBDV9bZZA/j/0TZbPbpp5/e/G7iUl1qyXqIYZJRQeCZ4AZMl8g3cAMDACAI4utf/3o6nb569ery8rKqqjRNnzt37qmnnnr44YfXmJHXFh48+diV0rgQnYiGKYosN+RWWzUtm6bJNbvnY8eOfeELXwAA27bdQbZJpQLYtnN3oaIaZjYRSUbDvg6AcKduZ6G6agcBIBKJXLx4keM4V4nVW744iEKEAQ2kY7EIP12oF6q93n+1UbJuSQFA0/RaS27L+miezibFIE4zXjUeukuwQdWi0ehjjz3m+iPB9vZNCADzLHV4MEUQUKxLqmEF2XUO1+HhYdcb2t3V4tUmttWfsdtqjuPcXSiruplxu6xnCIJw4cKF//Af/sO1a9cWFhZkWXYPp3zpS1/apl8DAIaEyCejgqJbU0tVx3GwF1FvbcsENeV5/vz5888//3ynALuJirF7tps+szbaLGygA9t8cwEAgGBoaOjs2Ye6BgLw1VporthoyXpU4NLxsBspb2WvvOmeAiE0Ojqay+UuXrx448aNYrE4MDBw7tw5N07kRm8F+XcWnCQIgaezcWGm2Co3ZM2wGP92w4Crv/zlL3/mM58BAF03XFE/m80wDENR1EaRSG0HtxR9udJ2MCSivBgOeSY2twO61cwtkzvIxsfHMcbttlQul+PxeCIRxxhveYDP7zKfeTAMpGPxCN+S1IVSc82zbp5btdXKw56FHUFDUtqKwbJMNi6IPAvYgZVYOt0TDMTJz3zmM+fPn3fPmy8tLQ8M5ARBIAiC5/loNLrlIMbeLMF8iD40mEYIzy1XZUWHDrEhSOTixYuuGOI4TqFQtG0rmUy6t7+uUuB7VhfAADbGUwtVTTNTMSEW2V4Y/kgk8ju/8ztPP/30xx9/PDc3H41GTp06NTY21uPpiZXSIBQX+WSUM0yrWG3rpsnSJPJMa6tWEZ9tQRTF8+cfPnPmTDab3WQh3yzXLY2Xnb/sZH+CATgu5B5u8wWAlYOzfjheWK42JEWLCqFULLzq7d6yZhhmbGwsFOKq1Vo+PxCP9+jwG0x5b3rwLDOeT82VmnPFhqQakbC3MwzUHul02jX/6rrBsCEAGMznXPdb5IdWxwgCD2WMsWFa88WG4zixCC+GGYokAJDHDZvul0iSdG8NAYBWq80wbCqVTKWS0Ku+0BNAASOMcCrCRQU3zmq7LasCH/Ifc11H0EolN004eAYDLtXkelONCeyRoSQAAOpo841WCl9kSCQS8XgcY9xqtRAih4aGIhGRIFDHQN+0LAgBxoARQ9Ouq1Wx2mq0FdO/Wrozu3g87topHcehKMZxrHQ63UWd4S1CGAFgx54p1DXT8tRD2wRCKJ1OP/roo/n8IMdxw8ND23cGx4BB4JhUlOdYSjXMUk3mGJah3cp3X5Ldva1rfNmuxrHHZ3YzyhPyg2d6v8KK0IexO0mgXG1LmhGLhLOpKHjaOeyHVO01C4qiOr2Mt0IXoTzE0sO5BIHQzEJFktVATeiW21UyuRYNgiR8kO41JCttilfWYYSQZlhTC2UTO8OZaDTMI9+lDXnzcsMKur3rZkD4+Xm59zbO3GZ0swsxZEzgwhxTqlRfePG1Srnq2M6qRyFgtM3TXDlJuVBqlGotgQvlM920f5un06VqxNqW3AyeKoimiESES8YERKBKQ2rL3WNbBu22phk7W9LT5mOMATuOs1BuaKY1mI6k45s5rWyEYEBSFHUPd/Bgb4xAVOAGM1HLsibnK4Zp4U0jKiLkNezO1Y0bYTepIYA/8taZrBBeKDXbsh4XuVxCAOxGDd+WR/29FGe9NM8y1FAmQgAu1NqK3hmxzg3ws9VaDd7BjM6jupphTi6UbcceTEdFPoTxqlz91X2TUiJ/27XFk+uAgx0TAizLCphKiMQLS8X/7//+fycn7/pnYRH44Z97SB93qDlQodaqNOVwiMknezL77zY88mUZcjyfZChqudpqtNWdpOjenGE7uC0bhWrLwU4utT1dw+7B2xVFwlw+GbMtZ3qpqptu0Lq9mva9YE+owcdaWcBxYKnckBQtGmZT0TBAcBB+b5tgDTVgAI6hR3MxIIilakvRzI6/9HKEGqCLphPrhnl3sWbbTi4REThmXfV7mu3bDCzYmbjHvpN3JhZnJiytJWvm5Hyp3W7bju1v8oIyb1XJFb0mAKBqU6lLaphjhtL7TQ2BPA0AFEkeHkwxNLXkXRews4QR6IZ1d7Eqa3o0HIoJXKBy2k8gwIAwICSGQ7mkaNnOfLFuWr1E7txb7BE1rBt5GABjWTNrLdWy7bjIpWLhjrM5fvDTPUMgz7v/cSF6dCBJEsR8odGUNMdx/FmJN5X916fr68AxGKY9X2pgGw1mYpEwi/yTDXAvcpEvPGyDKrADAIAmJ+9ociMZ5QmSpsNJhHyP4FUxv7dUNbh8jTEGx3YqDbkl66IQGsrGtleP3YE3TiiSGM0laZpcrjTrrQ3PF20J5Ou9Nd28M1uyLGcwFXWVMvcPOCpwQ7mY5TgzS1XD7D3cw15hd8LGdgGCFVUWBsDYAWe52pR1MypwmYQY5li8stbtLVb5HQIAAENT6USEY+hGWyvXJUUzBI519+vunWJbp+mNMJ/dEOiGNV+oYQfGBpNRke9MZBNNftdCdrW6bVQOrxF9tWF+cPAi4u1btdtL10gm7qAVlUFnaXqoIELgIIBaS623ZIwhHgknenMW3FUEl48BRaLRfIKhyXJdask7kBowACCMsGHa88WG7eDhbCwaDt0fAR573nbRMDeUiZm2Mzlf0Yytw7LvNfZIavAmzMqNggg5Dr41XVQ0PZuKpGKCd2DPfdhf1vamMCvmn0DdSCAUYqhcQiBpVK5LTUkHhNwLtXscH77G35UbsKabhVq73pJCLJVNhPkQ44mJ7tPeTRabK5bQ+s+9SA0IkGfYAgwAjz72+K997umTh4cIgiAYAZO0X17ovYV9HRBCCM0X6i1ZEzk6FeHo3jyCdhHYd5cFwDRFnjqUYRm63FCasn7v48XVumCsm5ZLDeNDqVhv1yPvPvxuD4foVIR3bHu52mrJyn3fU+yR1LDKOuauh44DE/MlVTPyqUgkzMLKJOwpeuLOgVZyA0CIpsijw+n5crPUkJqyOghRf+lFa8q/Dp4VEHlnghEAbknazFINIXIgEwnRpH9q2M0Qe7cS9VTIlTnsKtEVRVFVdaMrMBAghmF5gadI0n2VoelkjMqlomGeQzRJ0aIvVLjP9+RkhFa2d3ip2pRkLSGGcglhP2S8dSVxOwxjIEliJBeP8Ozccr3UaLdVXeS34Y+8LmWk6uaNmaJtOWMDiVi4x+uOdx+uxx9NkzGRS4hcTdaLNUkzrP0n4k7sJjXout5quR54DsDq64wx1gxrdrmmGVaUZ2kCt1oSAGAEhHv0cjvUoKqqYZqbRLNYB3eqO51GSkXRcgmBJsmlUn2pVB1K8t4OCOGVeQRgGIau6wDQliRdD25eAIQRJtwnESBcrjYWCjVAaCgt2qbRarVXSMZ/JUhzE0iyYpimomitVhsQmIY5Pz83Nze/0cU/CFA6nR4/clgU+A4ZEFMIUolIo6U0VaclyY5tu4KOoWuFYlFTdZfelpaWKpXKpUuX3NdCoVA6nfY9+Twpa3q50pT1uMDHRbbZbiF8T5ImAllRTMtSFBURQKBtJoJ8FyyARJhlKGKpVJ+aLxwa6AztvULojmPruu44tiTJtr2OVREABtvBy+X6bKGKAMI0skyt1erhCqL1RUOgyKquGwDIH//bgesu6/KDYw3lEo3JpenF2vHhOo51t5ioqrYPe59dowYEoCpatVrzf0UYOeAJ1RhhLOvWxGxJ082kyDLIrlZr7hadwHaP1ID8YH2youi60Wy2tn872wpU3YwLNEnCfLE2t1g+khG9W1aRDZgMJrNlWaqqAUC93qA63C6Ru0l0b0RAMF+o3F0oEQTKJ8KaolarDe8vGAARgO0e9m4YAGm6rut6W5IcxwEEpmEUi6XFxSXT3DAYr2lZYjRq6GKg2AEAxzJSEbZSl27OLI8PiLrAuX9tNurvvPt2pVLDGANg96TTz372MzepRCLxyCOP5HIDbhXdCt64u1hryUMpIUTiarWOtnOD4QoQaJpuGGar1dZ0leh544Y92cwB8C5VTUc5jqWKlcb0fCHCrIyKYBsLAA52ZEXFGCOipSjrtBIIY0CSYkxMLxqmGQ3zJNjtVku5p9CVCCFdNzRNt2y7Wq11lKe3TRxGQLiUhDRFTUd5BPj65MKpoShpx7q+0ZaUdQGudx+7JzVgoCgqCF+BABzfYRABBgfLprpUadm2PZhN5DPJEEsBICAw4WDcm+oPIc/abpqmYRgsy3Act5XwvyFIij4xlmUZulhrK5rFcSF39GGE/YXRzctSNQ0AWJalaSqQBJA/c1zbimHh+VKTItCx0Vw8KnJcyDV1ENA7NTgABMZYIUmGpkMchwCzDDM6OhaPJxxno50n5jg+FouxrOdS7fpfpuLCUCZ2fao8XWgASYU4V8eGHMceHh4WxYirTYjH47Ztu0f9ASASiUSjUY7jXBkeELZNe7nSbitaPMoPZZMcx90jNQBgB5MEwTA0x7kXSQTpbNaD/uYNe5dxA4wPZSK3FhuS1lQMjgsh79A3WkUNjq0oKsaYZdnQukOQLmHX28ZytU0gYiQXT8Yi4XC45+vaO2e7tzvTNJKmKY7jguttVj+/cZorZmUUj9qHB5OvXrm7WGpYDvZnU+frGANourF13PYdY6fU0LFzxRwXSiRi4FV2RXUPGJumvdTQZd3iOXYwm8jnUgThxv/HAATuRYMf5AjgOI5pWZGIKIr34r7mwnHwo2xI4JnpRtsCQoxGSAIhhDEQwZ1FGEDXvQ1FPBZlWGbF2A9uwEeEARwb20AtltsUgU4eHsxlkjxLg69vwAghby+zNSiKUlVVEIREIua+4HpMbw53nqPAFQHhId05NJhynNvzFYnnhWQi5opmsWgkFouapuGW54MPPqBp+vOf/3yQO8dxNE37GlZcq8uSZtoY51Kxw6MD3t1K2wcGoCiy3W6LohCJCL17EwdjyV1lHAwnDuUj4VtN2ZQNnEjE/VCKq2Dbtqqp2MHRiBgO8x3E4acJUGzolZZBEsRDh3O5bNIdutDLnShBOv7gZxhZ13U2xPqJbAP+TgkBACKZk+M5hIiqZNAstyY19xAdxmCZlixL281ou9gpNXRqtEiSDI4DYc/P06MG3dTmii3HcbJxIS7yXIgFAO/y9bWhErYGTVEkQbjRE3ZS+IEQExfDd3GtLmmybqZjAmCMEYFW07QbnoBhaNbLzjWmEP7IwG1Zr0taU9bSUW5sICHyHEn6qhZPclql5tisajRNkiRNU+w2qxYcZ7JtG2OHo4lYiLBse3qpZtoOQgRFkoggEQDHhTxlEIAgCBzHBYEMViUI2LFxoSGruhUTw7lUdLunj9ZAoymCQG6vbe+ggaeIBADkYDg8lBTDoZlCvViXaJoBT2m6qm1t2yYpEtsOTVMbDRLNcBYqbYIgTo3lYmKYZRhPQtk+NRiGQZIE1TH+t1E58JUoABGROzqcIQiiWJMMy6EZel1hMACiabIXV/cdYvd0De4swZ7i3pP+fbO7ath3///tvelzHMl16HuyqvfqfUM3urERAMF9xJmhqRlpljthjUKydf0ky8+OmPfC4Q/v3dAHf/Gf4f/ACtsvZIcj/O7zHSvkGEtjy5ItzQw5C4c7CZAASeyN3veu/bwPtXQBbIAguqsBYvIXE0Og0VVZWZl58uTJk+esFlRFySajQc4LXZ2L4PM0Buj7eYPZ6SQA6XiIc29tlRrr+Woi7Lfsb5plbSvaIgqNwL+I5Vpzs1hzOhwjsVCI87Js1z5p3Grfe6J7J4HuwTYduFqt3rp1q1gsVqq1W/fWZUkoV9Vf/ebKg4jj7OlTc3On0NgOInvujCIiEFRUfLRW4kUpmwyPxIIHXrtZ2THD72O/BK0/EgKjiVDQ7212hHyprqUC6r4EY3AD6GFa9rhvrdl5tFEkDDkxGvO4nYZQeI4K9nzy5w2jYhyaRQBwOZ2pWDDgdZXqrXy53moLmiOWeSQa9SgT+7/9wRnMgsJwuDe26IixKW7UghelpdWirMJ0Nh4J+sydROvo2SeG68FAzDBkIhX1+zyVRrtYbZvP342Loj8mMUrWf0AAgioAq32pXG9vFetel2NuMuVgGa0ZDfml3XFftTQP3u47kMG2CxGgWq1+9NFHCw8WREkqtxi/a7StMj/7+a8Tno7rf2fnTs5pAlzdVrte74UAACgqPlordgTp1GQgHuT6FgwEgOw4NfTss8PdTWfUWt3PeeJhv8/jrrXEta1KyJ/eYWjQLkMkZPd9EEGUitXGVqkW8PnG01GPyzkomz951jHzp1AR9MzCDCFejys7Eq7zwnq+Vqq1LAdnuzfXfhzI0+7BYBYUhruNDnbHFCEIgCiI0oOVgqwqY6lQ0O/W6tV9g5olBmAIFd7BdCYe5NzVBl+utdEY0cZRqN4PY5ifibFoglK9s1lseD3Oc9Mp1sGQA2l7XSG7S2y/XSBgPigC5/efP38+nkgAYrGhwCJ/81HR6Y+dORXPZMb0IYS4x5ixoqrqwspWh5dS0UAs7INdEjfbjj7d6CKCEJJNRqJBrtbsrOWrZ6etosFyESGG10kPyvX2ZqlOCJMI+6Ihn2Of6RX3fsTt4L68akHTGzT/PwLgdLAzY4mljXJec+vadkOzYxA4qDF4/wxgQWG1RGqfEOvAIqAoWG/xjzaLDgbGkuGA4axOCFhiFj93VQeiVk1n4yHOu1ms5soN6D72XhOkrg8Yzk4IpFhtrxfrHrfj5FiCZc3KGF80zP17P4nhsqlX7jnqYHyXEAiFQq+99pogCgQgV2rVXfduPymHEtmvv/7qzMy0of3s510TVUVekB6sFnhBSsWC8TC3awS75+F5JYvF7ttdm02mIsmILhqg2wO78TO6wnIXSrXWZrHudjpnsnG3kzUtmc9Y2+xPMhrz5TO/qN2TWKZW4mCZmbHkf365lCvVK41tnjvbnP3tPXIE0Ido6L5JUy5Y9QZjbAAAtHhxLV9tdIRULJSKBX1uh2UM4p4z9B6lD8bcMJoI+L2uYrW9XqhJsuxwOIwntz4QWv6v/Zmg4aUnK3K+3Ngs1ceS4alM3MEwO3abDqYK7bMX7lCjXS5nIpHQPvZw7TPTVcJ8WW0r/mDE2M3Z78NIipKvNIrVDkOYkWggHDj4PrHlYXu22jP39qy/EwDIJsPxELeWr6zkygC9RyHu2UNKtXau1PB5XWdOpB0sC91ZeK8K7t4ifXTFbfdETTR4nI6NQrVUbe1yyWA6/94M7AzFHk9abXQW14qEIeOpaMDvZQ3lzbQ7H0j9HsDBLASMhXxBzi0pSrHaKtdaRgAJYvlOb8zZrNbo5KsNQZRDfs9oPMjqtndzzBJCyH6edbtxad+O1bpRBIzn7l7l87jmxpIsyz7eKFabHd3TGvcaM5ZnQFFUljdLoqwko8F4mHM7WTC3pAfJM41qOw7CIiCkY4FI0Fdr8E82KjucHYn1m9rdDUuYtaRStZUr1n0e56nJEcOTbSjGvR6opvxDQIeDncnG3S7Har5aqDa1M8FPPR6xOZwCQB8FPGUI3BYwReuqepvVWp1HawWWIdOZuFfzdNJXyAQIA/saODtLH0igCwLgdbsS0UDA664126u5quWsaBfUXVJ2Fqc9eK7UKFVbfq9rbCTCeVxPWUn3u1jqcw2/XYUlAMTtcmSS4bDfU2nxW5Vmixc1m84exVgXhrwoLa2VFEWZysTCAd1jqr9XTnoJl2cJQfLUKyQQj3DRoE9S1K1Ko1RrgorYHT+ox6tBU8QbB1P10Qcq4lalsbpV9bqcp6eSWqi+4du5DIwWQQJIWJYZGwn5va5mW8xXWo02r/dGNKS69rv9Fh/bZA8xT+9Bo80vb1UYhj09meA8fXkiDBgkiDiWisQjXL3ZWc1XTHvWPmI26KNoLV/Ll5thv2cmGzu03tULhiFej2s8FXE5HKu5SrHSMGwfZG83Wy07cFsQ7z3OK4oykQoHua6T6yGCqAVnAo/HFQtzIb+nLUiP1oqq7junqQhG0h7CdMWZZhTS5mcCtWZno1ivtYWw3zuRijCspqATc9wNk24yR4KEAENIgHMmo36vy1mqtLZKdV390X0CjN5p/wamXaLBmGaJomK1wa/kaizDXJgd9XuPkmgAJIRMpMLJCFdrCav5qqYykO0qUO8r9X/J6lY1V24EOc90JmL34z4vDpaZzSQ8TnY1Vy1UW1pWvX2pJwRavHjz4bosK1OjsUjA9NgdNkZHQjAcSbTpdSQayMRD7Y64sFJUUZflVmO4FkXX/MDcCkOA1a1KvlwP+tzjIxGPy0H0+x7OHpmpsJgGaAJ4IhsP+t3FajNXbpqDtPuYQ3FssE1r0I0B2GoLuWK9UmuGfJ7J0agWKPeoQBAAxpKRWNhfbbSfbJa1VcJ+3ry2ZFIUdaNYK9ZakYBvbjL1PPGhhoHDwZyeTHpczo1CrVRrmyEynrm7Kitqtd5Z3iwDIVOj0ZB+OuvwlSLt8RExEw+OpyItXrz/ZEvVO5sRHsQ4xg0ELTXV1ueEAKwXaoVKK+z3zozF9fFGuhLoEDCtbvqPzOmpVCjg3ao0Ngp1SygeQowHHYI3pF2iwdwMypcbyxslhjBTmTjncVpyLB8FCABkkqFExN/mxdXNSqsjYvfh9wQBACvN9mah1ukIsbBvIhU7UnUDAJeDPX9y1ONybRTrpVpLixAHAM8cAs2WsLZV4yU5HPQlYwGv+9AFOrFq0YSQdCKUHYm0eXFxrSjLCnYHjy4hjA7YDVeuH9BCXN4s50qNYMA7lYlBVyLsS2gOHMtutZnmkcyNj4T83lyptp6vEjQ9gEHXe/bVQfvFZjsnwkap/mij5PO4zp1I9+1YYgtBzpMMcx6no1xrL28UVXX/O6P4ZLOcrza9HudILOjzuo7CvGrFwbKnJkcCfnex1sqXG7xgRhzcc4sOsdpoL64VGYaZHU+EOC+zbdtlqFjNj5alEImF/el4UFXUlVy51uwomiW/ewTTak+2SEMCoqIsb1XzlWYk4J0ZS3QlwjA2BHtgbjxrY177ZTwVDvq91UZns1TfHicSrbWzFfsCwOnm4M1S/XGu4vW4vjabdjw7zdSQQQBgGSYe9ici/iYvzS9vqSruS3lGAIAHy/lSrZWMBsZTEeiuV48KDEMiQV8q7gfAfKVZrpn75M/YFKg1+aX1EsuSCzOjXI/o2IeBdVsSgfO4klF/OOCtNTvLW1VJUrZvOgOA1YDQffhCrb1ZrAuSlIj4x1NR7G6a4BCCm++GmYuFAABiJOiNh3yEYfLV1kapTsxFLg7vCe0zQyIBkGQlV6yvF2o+j+vCyVHnkRMNuv6YigUzyUirI957sqWq+zlArR1zIQ+WC5V6Ox0LnhiN2/+0B4EATGfjQb83V2qu56v761ak0uwsrhVYhlyYGfV7XN242cM52bMHmnZNVJYhybB/ajQmycq9R1sdQyFCI31B90F1EaHPyI/WiqVqO+jzZBKBIOciurKuOYjgYVRQj+Oi/aLlInGybDYZjga5Uq21sJrXTbB6npIhSQc7g80jlqvtXLEmCFIi7J8YjTFHbUFhuGKOJkLj6UiT528/3FDVZ3YO/QuSoi6uFWv1TjoWmsrE9u3BMEQQAGA2mwxzno1C9Umu0v10x08WvUCQ5EKluZorsQycnkx5u84aQ9hNfwrc8W/3GSJB34lMTFKUmw83Oryk7/Hp23xoDPntVQRceLxVrrVG48ETo1FNjBA9dZ7mMXYYLUjQsC1qB5cJAoyloskwV6m3Hq2XNIloOOajEejEXuwZqwgEGCTkyWZ5s1CP+D3TYzHNU92W4g6M1iAI6VhwfCQiyerjjVKTF54lHQgAUVXMFWsbxToCSceD6Wjg8FXuXZjJxkOce71QfbJZsiyp0bKfoq3SdafBSr21lq8IopyKhtOxoLObuAWHs222DbL9X11AMYSQSMA3mY5KinJ9Ya3DS+Z+OWhmCWMaBsNwp21lzi9vleqtVDx4Ih03//TszWobMQNeYfcoBcB4MhwLc5VGe3mjpHdTtJgY7D9eZYto0IIsEoDHm6XNYi0S4E5PjhzsPKL9IBAI+b2jiVCI89Tb4pNceT8JQmRVvflgvdHmU7FgOhFyu9mjKBoIAJCpTDwa4urNznq+2ugIqMfA1GdINA57AmjRqGCjUF9aK3k97ldOT7pdjm1+iEdJLYoEvFOZOEvI4/XCVqUhSVqQUd33iegxv3VdTnMlbHWkxxulVltIx0Nj6SiAuZlhGJiOQv0IAMB4OjISCzTa4uONcrstakfSif7nF3hBAQAoycqTzfJGuREO+uYmRshQtKDnRVM7WZZJhP1TozFBUm8+3NieBbP3dZKifH5vtdnmJ9ORTCJ85BQiADD27OIhLp0Iul2OQrm5vFExzvyjrn4DaHYTY1zBar76cLXIed2vnMo4WIYAQXP37ChV0+txpePB0VhQkOX7jzcrzbY+clDzbSB6vCDUQ/Gpqvpks1Sstj1u52giFI/4zT3Ro9Ez9b0S7VESEX86FnQ5HMVKezlXUbUlj7m8sn/70p50uAgAUKw1H29WGm0xGeVms9EjNeHodFPPQTzMzU0kZVn+7M5KqyM84zoEXpBuPlhv89LseGJ8JGzI8qPQw3bicrAT6Wgi4i/V2g+X890/oB6zhnQd7YisqOv52kqu4ve6LsyktP3mozGZ7oRhSDTovTCbYQhz51GubKa6000GTHfvkgABlBX1+oONRosfT0XGRyIup3acxwyzc1htZ7WGdN+z28lmEqFULNBo8/ce57Q9dcMLfBgbRjZqDQ9WihvFmt/nms7E42EODe3uCIHdaTAW4ubGE7IsX59fbbSFvS3Voqys52tPNksMITNjidFEEACOouwDLRwAnsjEUrFQudaaX9lCVA2JaD4wmkc3y7X2ZqHW7gixoG96LG4ck8Wj13gAAAHOc/HUGEOY+cf5cq2tHaIwPLvI9lSqRJTkj289arQ6M9lYNhmyzME7Y08Nlx3jXF/9EIRsMjSVjjQ7wo2HG6qqAhoxhjRtyGZsszUAubOUK1Ua2WTo5ETS4WDJULSg58PYU0CASNB7Iht3sMxaobpVbgjiXuaGVlu4vrBWb3WS0UAmEfL7tCi4R05p0GcYxKlMYiQWLNZbC0+2REnS8w9bT4sba/KHK/knGyXO45rJJsIBL2F0/xTjlkeqhuj3uc/PpJ0M82itkCvVBEkyfRS6qYgREUFFaPDCl/OrTV6YycbHRsKmZ6WuOWlfPgTMonW/DAKqlr9lPBWdzsQbLeGL+VVZ0cOXd80iNmOPaEAQZfX24kax0hpLhGeyCcTD8ULdG9TPshEC6HE5UrHgRDomK+r9x/lKY49sq1hr8Z/cfCLL6vnpdCLi100WO7bKjgJGXO9MPJRJhgBgNV9fz9dA3RGskpiD49bixtJaIRH1X5wbM8z9hzty9oB43c4To9HsSLDJ80trpUKlpR8zIEBQJXrqCkKA8IL0aL2UL7U8bufkaDweCeh2BrC6HR+KZxex/Gc+ByLgSDw0ORoHwEfrhdV8VZQUY3f1hfWGRFRXc9UHK1uCLI+nopOjMWN2OmI6qWaQM2xyQZ/n1bMTLMt8Ob9aqOwa51+U1a1y48uFVVFRL57MjsQC+nr9iBnwAbojm/M4JkZCo/FQoy18Mb+hqKrVt1DXeBCaHfHhanGz1EiE/edn04ZvHmoLjmdm9B0+DGECPu/l8xM+r2dhpbiWr2rSEBFUgt29VgL1Fn/l1hNFVk5PplKxgINhtCVH94jFoTXftqB/Wshv7VF8Lkc6HhwbiUiyevXOkxYvGHLhxbA19HhESVY+ufW42mhnk5GpTCzImfr20epYxqSqn9QLcO6X57IsA3cXN7ZKdVnpnTCqWm/ff7S5UapHQ9yZE6lowGe06k5P3SOAPiEyBCbS0elsrN5sXbnzRFZU076gSzQEQnBxtbC6VVWRjCZCk+kYdFUhTek+ckoRALqcjktnxjmP5+FKYSVXlRRV24pFJJqZFQmoiJVG+5Obj2VFuXRuIp0ImduA25wFDkU6aDOTsfoxxILmukVGooGzJ1KirHxxb6XFi9jtY0dXNKAp5cB8TNQnmTYv/uf1h7VG58xUaiab6MZE6++1D9yJleiWKt3hxe91vjQzGg74Nkv1xxulWrNjqVlX58yV6p/eXVERL5+dyCbDbqcDQPdQ679bWR114EBV5nk+l8vNz89fv3H9xo3rC/fvFwtFSZamMrFTUyMdQbqxsF5ttM24acbyFRDxi/urG4XaaCJ4emokwLkAtBWXZpXAvkW7tvs5wLFHEMDlYF8+NRYLceuF6sOVfKnWJqbjpu7rCB1BWtmq3FncdDiYl2ZGEyFLrp1BhAvrC1PjBHMrqOthkYhwZ06MKIp6fX61VG3JWn7DoWwhDyRFDRr7dogAgiSvbFavP1xTFPXsVGoiFQHLbm0/2OM7YI5FdDkd6UTo/InRq7cf317avHR2PBriQBfUumgXZWU5V/lyfs3jcrx1cToS9BJi7lkOcAV4wPtIknT//v3r168vLi5WqhWWYX1ez8WXX37tta/HEqmZbCLo824WareWNl8/79Ey0JvBE3lB+nJ+rVhr/M7ZyQuzGZYxtIpB181Kn9HrCQDLkolU9OR4YnWr9GBl69FaIRUNguk2CQAI+XLj2vxqo82fHE9MpWN+r3v7PWxkHxUkO/61/iUe4s5Mpfxe92q+urBSGBsJR0K+4ciG/mNDEjRVHIIAUGvyv73xKF9uZZORkxOJWNhnbLYMeNv/6VigB7iHtiGkLSgIIZzH9dZLk37OfePB+oOVvNoNSaqXslGs317c3Co30rHA75ydCHAetPTBPqunOf5be5IlJckzLtQfb2Pjn/7pn/7lX/5lfX3d6/F6PN7FxYd///d//+tf/1ejVh1LhE+Nj7R56Tc3HteNHAfaDKUo6oPlwuJKQVbUkxPJ05Mj5t+MLksGssO0ozr7rOBuN9Pu4HU7L5+dSET9D1byNx6uyaol7BMBFdXlzfJHXz5yO51vvjydjPrZIZ7l6XM+83qc48nImRMpUVQ+vbu8pZvAjrKtQX82FQha8tMQRcGtcvODT+4qonz53PjUaNTlZBFt3Lfs59WjsRlkanEuF/v2pdlE0L+6Vb33OL9VbRgbfCwAqES9vbj+8c0lr8vx2vkTE+mwy8mAsVoclOx7evA88xLzO1evXv2P//gPj8fzR3/0Rz/60Y/+x//9P977P/7P1bW1f//lLxeXlrIjkdcuTEqy9J/XHpZrTUVRTG1AlJQPr8znio2JVPTM1EgsxFk3lYi2B6q9rIPXq/fHfVgwNGcLggBfPz+RTUY2Ss3bS1v5atMU+oBQa/EPVwvzj/N+r+d3v34y5PcetDjjiXFfBzQHsf5FQIyGuG/9zimHg/n0zvJ6viLLKgDgEY4oDfoKQjsJpi9FodJo33q4fvfRhtfpfP385GgiCHq0dUOKDwhTT+uvAcylvf4DyzJzU+nzMxm303V7KXfzwYYeiBQJAskV65/fW7n/OBeP+L/3zfNuPSspGil2+j0mslsOxf3fwel0vv322++999677747Ozs7Ozvzgz/84dzs3Mb6+ubm5kgs8PKZ8ZDf8/Bx/vbDzapmTCEoKcpGsf7vnz+sNDuvnZ88dyJtPXrVfbznzE76VO12/ctBb9kNtjCViZ2fToc479Jq8dPby7pDBwAgPFwpfDG/ohL13MzI6cmUz7aIVd0TXUaKyoHcNBTwvvnSVCTsW8mV7y7mCpWG7pNiMwcVDdpAAIYQxjTPy4rycKXw4ZX7sozn57Knp0eDnNecZwYbz85c4ffXAESviOF5SgAYwG+/dmoyE1lczV+5+Xiz0FAJIKitjvDrL5Y+v7vqdDrPn8xcnEs7HE40m2inf+HAeHZWyG4oEvzOd77zF3/xF2+//bbT6QQABOTbbUVROJ/P43a7nOzYSOjNV2ZYlvnF1YWHK2VJRlWFQqX1wcf3Hq4VElHu5dPjY6moZTLXl+vao/RdFfLUCqIfKyAx4ya6neybF2cuTKfWtir/dvX+aq6mIhCEYq155faTa/dXk1H/D965EPJ5+x+xPdMOWlWJ/lZJ228L4HKymWT48pkJh4P5zfWlmw82JEm2IyPIDvrUGkCbSAigimQlV/vo5qMbC2uxEPe//bfzI9EAYRjTQnnU/J3A6JL6kNaP2RBAcuns2LkTKUVRPr2z/O+fLTTbYq3NX7395Bef3H+8UTo5kfzu62cCnKubgLBrpetjdfNUY++ze5kdkRDi9Xrj8TjHcdqHnXb7408+XltbO3Xq1NTUFCEkEeb++zfPxUK+awurH91aWi82y3X+4xtL/+tXX0qS+O3Lc2cmRzwulhjZuYxFxMF3TLZX6PnS/O7jlsaSh5Dz06mLc2NOJ3ttfuVnv7lTabSLtcavrj38zy8X623h9GTqzYszLofDJr80M43oIFUGffoFzuv+3jfPZRKh+8tbv7mxtLhS2kdUkX454A6FMaGgmTCp3hY/uvX443s5UZZePz/5+rkxj5MRRRG6I1Alg1ggIYAky7IsS5Kk3b//GxLrzwgBD3vpTObBcm5xtfivn9xXZRERf3tr5fZiPuT3XD4z9spcRpZlAEW7GLt17HcHU5IkRVFESRYEkRBQVbVWq9XrdVVVd7vE5/OFw2GXy2XtjoqiNBqNBw8W/p+f/CQai772+uuZTEYUBQaUsZh7Iu6+s1z5xZV7xZU635T/33+7/mi9EHTiS5ORCOeUJVnb7UctYw925V4/dRMlWVVVrdWMYJN9Ydo+CBIk6HWz52ZS506kP727/LPf3iY4ywvCJ3c3FlbKY4nQNy5MhTinLIuGnjEwEEGSZEVRZUXVWm2A9wYABKKq+OqpzCsnM//xxYOPbywRiX/74tgAi+nJAUXDzhkS8dFm9Yv59Y1iYyod/d1XpjgnNJsNw4dD+7rafyhc7Xxtq9USJaneaMqy0s8dEbTkld2KmOde57LhS6dGy7Xm4lrxf7V5ANgo1r1u52vnspdPpx2qXK3WkABRrVKB6KPp4JBWqy2IYqvVcjhYABQF4f79+/fu3dtDCI6NjV28eDEajZqfSJJULpfv3bv3ycefrK2t/fff+/2ZmVlZUarVWrPVery4ECXVoFNZ2Sy0ZD86vPee5LysOumXOpX1SimhRW0ABGBkorKGNUU7YcXAAbU/0mq3RUlqNJsqKsw279gDvjJNmWGQEACFqECYsZjvtbOjq1ul1UL1p7+dlxW1VOtE/O6vn8m+PJ2s1+sWF4J+sag/pNPheZ5XVKzWaoAqAGMchOq7FABN73YQ+Pqp0dVc6eFa6ebS5olMuP+b700ffg2oWxi1XNcrhUZHVC7MpL9xduxrsylZEmXZnFB1SYJ9b1QgAUQiipKiKIIgEOhL2PQWDQCAJMK5v3F+nBDy6fzG0moBgExlYq+eTL9+fmwqFep02tppvW4SlMGIBkYQRUVRJEnsdDpAUBYlh8MRCoUkadcQEl6vV5blTkc/9KEoyvr6+ueff/75558zDPu93//e22+9FQoFOx0eAJqNRiGfy4QZty+2xTuWGEZRcTYbjTi9CUeNb1XrjbrX59OXgURhVAb1WmqrwoOLBkEQFUURRZFhgenuix58H04P6IhAAFUCKmE4N/vyyXRHkq/e23jwJM8w7HQ2cel05rUzmWTI0+kIhKiEsIZrfF+YooEQVhAEWZYJw/AdHlEBYAxbWN+laLkziILInJmKf0c4Fb233mg2G+0B6Mt700embIsdEIFkE8Hvvjb3tdNTJ8diAa+NaQsQAFVVluWAn+M4n22lkK8FAtl08tzs2O2FFWDI2ensuRPJWMjHMnZZhxGBZVm+0/F5vaFQUCslHo+//PLL+74Dbm1tXbly5be//W0ikfjhD3948eJFt9ttKvBul/Pi1742d/IkcXqrPPMP739Qrdb/r+9/P+SUVKnl9XjT6XQgELCjdqyj3Wq1OJ/PH/Dpu1Z9+/xaLKWgAmEAAwF/eiRxbnb8xt0lwrjmplJnpkaSYS+j7bSDyhxcuu0GcTqdoiS7XK5gKGiJ4dZ3KfqyTgteCeFQIBqPnZkde7yy6WGeHYisTw5sa9A0TG1trQKyr8wkOG7ixOQEGCllbQIBRFHieSEQCASDtnRi0A0QGIuGJ9KxCxNhQsjoaNrjdurOUTaVCsAwbL1e5zguHA4foJR2u/3FF1989tlnyWTyz/7sz775zW/CNtUXwuFwOp02vo6f//qny/Xi77/5kvEBANjWeoSplCt+vz8cCvY08j8/aGkO1YjwiLEojqXjZ0b9CkIyEfdzPnPziKAKZMAeAYjgcDha7bbb7Q6HQoPsHFrATqJtoakEmDBAZiQ6kfBtbuQGV0xv+rU16CFACBKiEjDPs9goGnRN1OZ9XdJ1mUHD41NPn2aXz7BZdB/j5ubNm//4j/+IiO+++24gEFhYWDDlQiKRsNoj0LAq4g6BQOwSD+ZWAgys+YhhJ0ViTK3GEkNFYBElRM2UT1DbjUMy8N5pdBPVDGY9uM5JEBBQBcISzUIOWkAkVO0/qdjfGQqCCCoAQyzH14azSWn7izF9obb14wFvvQ2cq1evbm5uRqPRR48e5fN5sGxtvvPOO6+//jpAdyABAHRPF6GxiWs4cA2enn4Nfd4SALScIHrWOs3ogwCAKgHQQzboNbSx8axODQMry2gJBMvd9C55VDcvDQgBRt/HNULp254sDwD0lhhcG/QqwWwKYyI1px+wTzQdoCrWjXS/33/x4kUAEEWxXC6DRTSYdkprejiArsuCvptkp05kjJ8dBfRXJOozqdliRM9Tg4YbNRrHawkasW0OXtwuWDvh4PqkZv/VDr0a0lz3pTnqokF7+7jNjcTe9YTOgLwh90LvsN2DlQM7JbFXoeZA3TfWefiNN944e/asuZ2h9VHt/1NTUz0KQ91e1tUVbJN9eiSsrgOp/nHfKzTDltmVa9oiF/QW091vBsZAnZr2A9n5loZScj+iAXWPDNPyMNzAwza7ihKLB7K5CW+zmQHgYJZAc/yfOnXqGXfvOaERgENbKPVZqn6Gh5grC3OhhAyACkZKKs1QNJDF0jPf1ODWFLrSQLaJNzR8+u2lj1Au5lqVgLG/T2zyQu2JcRDangLR0LaN8HCgnyXrdfBoIAX2Vrb3e+E+e6HlCBAg6bp06Kt0tPihDJrdnrCPBtRqjmCq2EZkaO3UnxkoWl8qabUbVgfdcdrqgOza347ugsIw7egaKDH2Jmykpxi2a7Iz1hLGz2ZZ9lkZetx5PzPPwd6A7o5idDDU62Z3A+6sTn9Tq3YlYzjWdZtLW2/qaXe6xkrdxD80+lx66BcbViDzMxzKFNxvlCeLgmb7QugwVF4CwFgWFMN+AHurTHr+aGN5T29PDKKCPQWaVta2b8HQ26/P2pkDy/LsugVlCMr5AHcTDmepajukx0/Hh+NYp2PPcBrtiGW1p1AoRwMqGigUSg+oaKBQKD2gooFCofSAigYKhdIDKhooFEoPqGigUCg9oKKBQqH0gIoGCoXSAyoaKBRKD6hooFAoPaCigUKh9ICKBgqF0gMqGigUSg+oaKBQKD3oN5QL5QgiCEKn09GCx7Is6/P5XC7XQDLQUr46DFA02BU0sXdhuGvmaDtKs/x/CGX1VRDP84uLi/fv3y8UCgzDeL3eCxcuTE9PBwKBw06hsVu9bArGO8TueBzpI+clwLYWHWpD6GHLh1DSsKK+7UiUeMCqIeJHH3304YcfPn782Ol0MgyTy+Wmp6ffe++9V199leM42DMco/0ZePCp26ORFGzgJW0rwwy6PfiS7OQQn7mPsLHb3zgZVjxOLS4wGXTmwj0hlv/bWgQAMAAE8bn7hPb9jY2Nn/zkJw8fPrx06dKlS5cIIVeuXPnnf/7nUCg0MjIyNze3d9I8m3shMSWtNQO9XXF/zaCxRhn9lzT8gbp7cbY/Rl8LioHmL3y+QrUfh1mu3egSlmzrzftH+/7y8rLL5fq93/u973//+xMTE4j41ltv3bt37+7du0tLS8/MUjEEhpvfZcCl7DlQu38ypswBz5ZdwYTE5uDtAP3bGkzFAQCGPFZfNN3wGZh5TaCPkZPJZP7kT/4klUrNzs663W5E9Hg8sVis2WyKojjIxz3yIPZrtXmu0p4ua+D9s5vYAl6IYPOm4jDUgTrMVofhmiH7IpVKRSIRl8uFiPl8XpKkYrHYarXGx8cTiYT2ncNbvmIvW4NdEIKqisMxSFmx4/VaJgyzOkdeNHRBUFFV1WFsHCAiIqgqDqE4VVW13jWE4hBRVVVEVFEvCxF5nud5fveiicvl9Pl8LMsCgNPpdDqdALC0tHTlypVms3nt2jVCyOXLlycnJ7WbK4piDhhZlhVFEQRBvxchLMvaJDhUFWEorxEAVK2qgIjDKA4NzFYb9P0BoJt8YjjybmCiAQFlSe50+EHd8GkIAVVFIEQQJVlRBEHodBy25qFEQFEQRUkCgA7PK6pip3aEiCAIgqIooii2OzwBFEVxYWHhwYMH5uh9CpLNZs+fPx+JRKyL26WlR7/4xS9ardadO3deeuml0dFRj8fT6XS0DNrm3SqVSqPRWFpa0n51Op3RaNTj8Q6+bqBVTdVajWGsi/PBt6CqKqIkAyLPCwzDDvbmAGCZtAkA8Lwgy4ooSu0Oz5gZ9AZeJOq5vkVROupmSLCoTwRIq9XO5wt2Kqv6O2+12jzPV6q1TqdzsPyx+yoMEAAkSW612gBQLJacTgfYlf1Nr0WH5zu8QGp1SZIJAUkUt7bym5u5PUSDw+EcGUnJsrJdlSWTk1OKIqdSqSdPnnz66ac+n29iYqJWq3322WfFYlGb3+bn56vV6vvvv69dE41GX3755VQqPfD3iQA8zwuCWK3W2p0OQ6xZAu0QDWqrqfUN0my1rUJIo7/ydmbFEgSx3e6IksQUisTskPq/ffZP4y76mgIQodFsDTT1d28GY2vQQDNnrK0Yqdg1Dc76qR10hxrRFTs7Xbv0fK26CQ3B6XReuHDh3Lnze1aQMAzRXoX58ufmTs7OTquq2mg0/vIv//LDDz8MhULj4+PagkKWZU00aHq3LMvaVapqaOL21FHP7WpMf/atnBGREEBVS1+sPn33wZWnd0fUEyebZaHupYLdr/VZCpipg1+wBQWBUCiYzWYGdcM9KBZLDKmOJOOBgN/usgRBJEweAFKpEbfLaXdx9XpTVeRoNBKPxw5w+fz8fKVSGRsby2az2ieKorzyyiu3b98WRXFsbCyTyUxNTSmKov212Wyura39+Z//ufYry7Iej0czWwycer0hCmIiHg8GObu9thVFJZs5VOV4PO7z+WwtCwBarVY+D263Z3Q0ZXdZALC1ld/ayttdyiDPUDAso9nA7IZlWYZhHA7HEIpTVFXrx86hFOdwOA5QNXMpcfXq1V/96ldvvvnmH/7hH8ZiMUJIo9Eol8uax7R2T5fLZep6Pp/P7XbHYgcRQ8+Lw+FgGOJwsJqbpq1lMYzCMowKQ+okWquxw+r/Dgf7Qu1QUA4bREylUpVK5Ze//KXH47l48SLDMAsLC9evXz9x4sSJEye0r71wzsKUQ4GKhmPFpUuX3nnnnatXr37wwQfXrl1jGCafz6uq+u677164cOGwn47yIkFFwwuP9SRLKpX6gz/4g6mpqQcPHuRyOULI7Ozs7OzsG2+8kckMwwxEOTZQ0fDCYz1TiIhzc3MnT55sNBraoexQKBQMBh0OvaFfxNOHlEOBioYXG+uZC6v6EAgEAoGA9h2rLKBygbJPqGh4sXl62O9xHJaqDJT9Q4OCfYWwnJGlUJ4BFQ1fLajWQNknVDRQKJQeUNFAoVB6QEUDhULpARUNFAqlB1Q0UCiUHlDRQKFQekBFA4VC6QEVDRQKpQdUNFAolB5Q0XD8sTpHaz9Td2nKM6HHq44/1qMTL2hWWMrwoaLhKwE9l015XuiCgkKh9ICKhmMONStQDgYVDV85qLCg7AcqGo4zWo5Wa/5boLYGyv6gouE4o6pqLpcrl8uiKJofUq2Bsh/oDsWxpdPpLC0t/fznP08kEu+88874+Lj2OdUaKPthYKKB2JVC9fB5EUeSqqrr6+t/+7d/+/7778/Nzc3NzZmi4bDpmZt2SO+4f5+OfdzB1uoMKNf3PhjkgmKYQ2iYWvHQhJ6W33kg1Gq1mzdv/uY3v+F5vlarWRcUe5Q+mLJ3L2EXuWBfcTvfpm1ygdjd/Y3WIQAEkADaPtroguIYIorinTt3/uu//iubzSKiy+Xa7ZumOBiWi+Twpg/DJXyQ99zTlxQt/+8+w0DeqiXDiPkots9WL6oZcngLZuzxk00QQvrvyoi4urp69erVXC73x3/8x9FodP9pqW1WHIhRirUgu9txwDXaUy4cK14s0YCI+JR4trVV0PwPh1GWWaK+7wiAqqrKe7Jjb5Ln+U8++eTevXuvvvrqm2++ybJsj5IsRyp2/GCndOi2nWV82VYg0drMDtGDRvugRc/XSzU/HJDKgOZ9CNGWLQRhGLJocGZIor8wsHNKJ0RbQKJlCJkfDhwE6K4iSfdD28oC0N6cqTrKspTPF7e2tmRZ3u3KcDicyWR8Pp/2661btz766COO437wgx+43e6eHfRpQaB9zW5dTBsyRikIQOxrPtRepg0V0t6ZNlqNF9h9jbBnArEDlGXpEsRcJw1hQTEw0YAInXa7VCoBgI1aIgIQaNRbnY5YrTZEUbKrIANJlNotHgDKpYrT5bS7uFaL53mxUW9qA5Xn+fv37t+9d1fghd0uGZ8YR4RoNAoAzWbzf/7P/69Srv7ut74VCIRKpbIkSaIo1Wr1YrEEAO12a2npUavV1Ca3hw8f5vP5n/3sZ1o/5jhuYmIiFArbU7WOJErVakOWFMIQcxTZYeZQVbXd4hHRWanxHd5axACL02+F0OE77Q4vy2qpVB7InbcXY5mXEAmBRqOF9ltt+hINO95yq9XO5/MAxK51CuqSmOd5QRAqlWqzabsZVVWUNs8DAKgq00s5HxgIQECSZIEX6giCKAKAKisOhyubGZMVZbfrgsFgs9GWJRUI/NuH//bpp19MTky4XO4vv/yyVqvWag1JEufnFyKRaDAYrNWqv/zlLzc3N1VVIYTMz883m833339fu9XIyMjbb789MTFlh3CXJEkQxFq11mm3dSXTGK2DLw6x1e4AICqKw+FEU//eof4fCAIEAc2nJkAkSWzzgsBKqqoCoL59MIg6ETA0Bcu76nQ6QzDo9jW0doj8QDAwOpoaxFPtgq4jQqVcqdUbiXiM8/tsLA4AAERRKhTLAJCIx1wuOyURAhBoNtvFAoTDwXAkBACoQnp0RJLlPVbkLOtwOR0MwwCBa19+3mrVRUlYWlpcXn7carVqtaqiyPfv35uZmR4by6bTqXA43Ol0tFHy4x//OJfL/ehHP9Ju5fF4kskkx3F21K/ZbKmKEk/E/H6OIQMbPD1RFMwXCqgqkUjE6/V2156mHDpQ0YZ6T8AiGgBIu90ulcout3skGQcw/jiY2umiwXq3YqlcLlcGcvc96Levd7UGAm63OxgM9vtE+4Dn+Q7Pc34uGAzYXpYg1BtNAAgE/G73rruAgwKR1Go1r897sDcZjUamp0/4/b5arQIAnU5HFAVFUer1migKXq8nmUwkkwnz+x988IEsy5cvXx5YBXYHERxOB8dxwWBg/5smB0NRlFq9jqrM+Tm/PZLOCsOQRrPp9Qyp/7fabWK/HXJwtgZ4Md0Gjxc/+MEP6vW6Ka/r9fq1a9dEUXz11VfPnDljkzpwNCG2LFT2Km5oDKcs6vJ0fEDEt956y7rEKxaL//AP/8Dz/De+8Y0LFy7A8FybKC88VDQcH57eM3O5XK+++qooitFo1O59Zcoxg4qGF5ueA9780Ofzvffee6qqjo6O2rF7RznGUNHwYtNzkJsfsiw7MTFBCHE4HHtfQqHsgIqG48PT6gAhxOVyUVlAOQAv1hkKyl7spkFYXP0plP1CRcNXAqo4UJ4XKhqOG08rCFQuUA4AFQ3HDSoIKAOBigYKhdIDKhooFEoPqGigUCg9oKKBQqH0gIoGCoXSAyoaKBRKD6hooFAoPaCigUKh9ICKhmMCPSVBGSxUNBwHzDOXVEBQBgUVDccB6hxNGThUNBwf9h++iSoXlGdCRcNxYI+4j2b+xWd+k0KxQkXDcUCL17L3F3b8QKHsDRUNx5anFQS6jqDsHxob8jigWRkQkef5R48e1Wq1HX8dHx9PJpMul4uGk6bsEyoajgNm8tFcLvfjH/94aWkpGAyaggARv//977/xxhuxWEyLE0mlA+WZDEw0EED70/B1sSQPHmb6siFwwJeojfZqtXrjxg1RFE+fPh2Px00pkEgktHjzhy4UCCFPLWtsaUEEAHi6LLsYTqWGyQC1Bjxwtz7KkGG1cD+TuXmtLMuqqp49e/aHP/xhNps1vxAMBn0+27OKPwtzr2Q4/eTYmlZwKAlm+xINO3qz3RPSjuKMbTnbyx0ORtUOIh/MBYX2TlKp1OzsbCgU0j4khFgzU+8hg4aw1rCoeya2lIiDy2O/H3YUZV+31OUCHm3R8FQ+tf6eZU+2+wJrPb7HM9hQLhiznL1zkFFB9QBpI0y50Gg0JElCxFwud+vWLVmWfT7fyZMnw+GwmcDKlCBPb3na/DIJIWC0Ybc1bSqUEEBEU+wM08LytN96n0Vb5T4hBACB2K4RDWxBYbfyZt2Z19+OoaDa3OTdguwsBYzOpJdoFsfzvCAIqqrudqHL5fJ4PA6HgxCyvr7ebrdv3brFMMz6+rokSZIkvfPOO2+//fbk5KRpmDykAxeIqILRglbxZEsLErQucu0oYvuT7yxrgPWyviXjvQ3kxnsxGNGgPbckSa1WayA33JtOR5AkudPhWZa1tSBEEEVRFGUA6HR4WVZsbhLC84IsK4IgttttAJAkaX19Y21tVZKk3a6Jx+NTU1N+fwAAZVmJxxP1eqNQKExOTgLAtWvX/uZv/qZcLn/ve9+bnJwURbFcLguCoF1bLBar1erdu3e1X10uVzQa9Xg8dtSt0+FlWeV5weFoM4z1PZKBa2SqqoqCjKh22jwBxhDutowoROh0OpIkM4zUbLY1oacVNNASu0Z3SRIJsd0jqV/RYM5CbrdbEIRCoTgE22ynwyuKUqvVO52OrQUBgKIooigCQLlcYVl724MQIgiioqitVktRFACQJGltbW1xcUl7hp40m22v1xcOC4iYSqW+853vOhxsNpuNxWKI6sTExF//9V///Oc/j0QiHMdVq9XPPvusWCxqk8/CwkKlUvnpT38KAIgYi8UuXryYSqXtqJ0oitqSh+c7201Uz3DlPACIKAoCIlartVarbYiewcsg7baadqaqWCya/X/gBTGGYkIEQfB6bTcq9ysazDaORCJGk6NNTpaISAggAss6OI5jGMZqXbMNdLncAMCyzDDMwg6n1+s1DYcOhyOTyfh8nCYpeuL3+4PBkNPpAoC5ublsdszlcvp8nMPBIqozMzPXr1//13/9183NTZfL5fV6Y7GYqW1xHMfzfCqVAgBEDIVCHMe5XC4baopOp9Pj8bIsSwhsHzx2vFV0Op2IwDCMPetNTTXQ9Xyn0+nxeAgBhmEBkBDGhsVadxHtdrtcLls0OysDWVAgAAmFgoEAZyyVbbI566LBVK4OfZfeBna+vUQisa/LEAkhnY7X4/F4PB6O44y7QSqVYhjG5XLFYrFQKBQOh83lyZ07dzwez7e//W2tlzscDr/fr0mZQWPO2y82ljU/mJUaYjfUbPAMy9rurDiwAhwOFsDelT8AHJsethsHtl1pF3722ae3bt06f/785cuXnU4nAPA8v7y8zHFcPB53u90ul8uQGgAAgUDA5/NZPSAoe2NtoMPwK7VV1drGQETDMN/OsRUKGgfuatqFS0tLf/d3f3fq1Kl6vZ7NZhFxcXHxiy++OH369NzcXD/3p2jssJIMv/yhlUTPUBwrvvWtb83Pz1+9evWv/uqvpqenGYa5fft2LBb77ne/e+bMmcN+OsqLBBUNxwFTs00mk3/6p3966tSpBw8e8DzPsuwbb7xx+fLlCxcuRCKRHV+mUPaAiobjgNVUPjMzE41GL1++LAgCIcTn842MjHAcp+1KmH51VDpQ9oaKhmOCOdSdTufIyMjIyMjhPg/lRYdGeTpW7HM7naoMlGdCRcMxoWc82KclBRUKlH1CRcNxoKftYLe8Ncc2jAFloFDRcBzoqQvsFkWaKg6U/UBFA4VC6QEVDRQKpQdUNFAolB5Q0UChUHpARQOFQukBFQ0UCqUHVDRQKJQeUNFAoVB6QEUDhULpARUNFAqlB1Q0fKVhWVYLIUmh7IDGa/hKMzo6aneaH8oLChUNX10Q8fLly+12ewgZKCkvHINPHER5gdAySrndbqBygbIdKhooAFQuUJ6CmiEpVC5QekBFAwWs6ZgO90koRwcqGig6VHegWKGi4auOqSnYkcye8uJCewOFQukB1RooFEoPqGigUCg9oKKBQqH04P8HYuy/pRxj80gAAAAASUVORK5CYII= | The given graph is of the form $y = A \cdot \sin(B \cdot x)$ or $y = A \cdot \cos(B \cdot x)$, where $B > 0$. Write the equation of the graph. | The equation of the graph: $y=-2\cdot\cos(\pi\cdot x)$ |
3eaa5161-484b-40de-982c-87a1aec7f5d5 | sequences_series | false | null | Evaluate the sum of the series $\sum_{n=1}^\infty\left(\frac{ 1 }{ n \cdot (n+1) \cdot (n+2) }\right)$.
(Hint: $\frac{ 1 }{ n \cdot (n+1) \cdot (n+2) }=\frac{ 1 }{ 2 \cdot n }-\frac{ 1 }{ n+1 }+\frac{ 1 }{ 2 \cdot (n+2) }$) | $\sum_{n=1}^\infty\left(\frac{ 1 }{ n \cdot (n+1) \cdot (n+2) }\right)$ = $\frac{1}{4}$ |
3ee1b980-1888-485a-ae03-fd08a495dbd8 | algebra | true | 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 | Using the given graphs of $f(x)$ and $g(x)$, find $g\left(f(1)\right)$. | The final answer:
$g\left(f(1)\right)$ = $4$ |
3ef90475-04a4-4e4f-9125-9db390b3a277 | multivariable_calculus | false | null | Determine the coordinates, if any, for which $f(x,y) = 24 \cdot x + 12 \cdot y - 8 \cdot x \cdot y - 4 \cdot x^2 - 6 \cdot y^2$ has
1. a Relative Minimum(s)
2. a Relative Maximum(s)
3. a Saddle Point(s)
If a Relative Minimum or Maximum, find the Minimum or Maximum value. If none, enter None. | 1. The function $f(x,y)$ has Relative Minimum(s) at None with the value(s) None
2. The function $f(x,y)$ has Relative Maximum(s) at $P(6,-3)$ with the value(s) $54$
3. The function $f(x,y)$ has a Saddle Point(s) at None |
3f0c9f6c-3adf-47e7-abca-d957dd1b58e5 | sequences_series | false | null | Use the substitution $(b+x)^r = (b+a)^r \cdot \left(1+\frac{ x-a }{ b+a }\right)^r$ in the binomial expansion to find the Taylor series of the function $\sqrt{2 \cdot x-x^2}$ with the center $a=1$. | $\sqrt{2 \cdot x-x^2}$ = $\sum_{n=0}^\infty\left((-1)^n\cdot C_{\frac{1}{2}}^n\cdot(x-1)^{2\cdot n}\right)$ |
3f25f089-28ec-4e69-9844-a0fec7031aee | multivariable_calculus | true | 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 | Find the surface area bounded by the curves $y=2^x$, $y=2^{-2 \cdot x}$, and $y=4$. | $S$ = $\frac{24-\frac{9}{\ln(2)}}{2}$ |
3f5c9b71-a742-4303-afc0-19085f5bde1e | differential_calc | true | 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 | Use the following graph to evaluate:
1. $f'(-0.5)$
2. $f'(0)$
3. $f'(1)$
4. $f'(2)$
5. $f'(3)$
If it doesn't exist, then write $\text{None}$. | 1. $f'(-0.5)$: $1$
2. $f'(0)$: None
3. $f'(1)$: $-1$
4. $f'(2)$: None
5. $f'(3)$: $2$ |
3f808070-9259-416b-a36a-b19055958dcb | integral_calc | false | null | Solve the integral:
$$
\int \tan(x)^4 \, dx
$$ | $\int \tan(x)^4 \, dx$ = $C+\frac{1}{3}\cdot\left(\tan(x)\right)^3+\arctan\left(\tan(x)\right)-\tan(x)$ |
3f809052-b6b6-47df-b4fc-9b20684a67e7 | sequences_series | false | null | Find the Fourier series of the function $u = \left| \sin(x) \right|$ in the interval $[-\pi, \pi]$. | The Fourier series is: $\frac{2}{\pi}-\frac{4}{\pi}\cdot\left(\frac{\cos(2\cdot x)}{1\cdot3}+\frac{\cos(4\cdot x)}{3\cdot5}+\frac{\cos(6\cdot x)}{5\cdot7}+\cdots\right)$ |
3fae81c2-34d5-40d0-a54b-acbf74cc2037 | precalculus_review | false | null | The cost to remove a toxin from a lake is modeled by the function $C(p) = \frac{ 75 \cdot p }{ 85-p }$, where $C$ is the cost (in thousands of dollars) and $p$ is the amount of toxin in a small lake (measured in parts per billion [ppb]). This model is valid only when the amount of toxin is less than $85$ ppb.
1. Find the cost to remove $25$ ppb, $40$ ppb, and $50$ ppb of the toxin from the lake.
2. Find the inverse function.
3. Use part b. to determine how much toxin is removed for $\$50000$. | 1. The cost to remove $25$ ppb is: $31.25$ thousand dollars
The cost to remove $40$ ppb is: $66.66666667$ thousand dollars
The cost to remove $50$ ppb is: $107.14285714$ thousand dollars
2. $p(C)=\frac{85\cdot C}{75+C}$
3. $34$ ppb |
3fc943b6-d10d-40d3-965c-2b98d04be288 | multivariable_calculus | false | null | Calculate the area of the surface formed by rotating the astroid $x^{\frac{ 2 }{ 3 }} + y^{\frac{ 2 }{ 3 }} = 2^{\frac{ 2 }{ 3 }}$ about the x-axis. | The final answer: $\frac{48\cdot\pi}{5}$ |
4050b38b-62c7-4952-b909-c0012fe5130d | algebra | false | null | Use the properties of logarithms to expand the logarithm $\ln\left(y \cdot \sqrt{\frac{ y }{ 1-y }}\right)$ as much as possible. Rewrite the expression as a sum, difference, or product of logs. | The final answer: $\frac{3}{2}\cdot\ln(y)-\frac{1}{2}\cdot\ln(1-y)$ |
405af248-578b-4765-bfd1-52a2223805d6 | algebra | false | null | Multiply the rational expressions and express the product in simplest form:
$$
\frac{ 2 \cdot d^2 + d - 45 }{ d^2 + 7 \cdot d + 10 } \cdot \frac{ 4 \cdot d^2 + 7 \cdot d - 2 }{ 4 \cdot d^2 + 31 \cdot d - 8 }
$$ | The final answer: $\frac{(2\cdot d-9)}{(d+8)}$ |
40a59d5b-7cc2-4527-8be9-d64c434be864 | multivariable_calculus | false | null | Evaluate $\int\int_{D}{\left(\int_{0}^{4 \cdot x^2+4 \cdot y^2}{y \, dz}\right) \, dA}$, where $D = \left\{(x,y) | x^2+y^2 \le 4, y \ge 1, x \ge 0\right\}$ is the projection of $E$ onto the $x \cdot y$-plane. | $I$ = $\frac{274}{15}$ |
412a48cb-7490-498f-ae2c-160d74d3e912 | sequences_series | false | null | Consider the function $y = \left| \cos\left( \frac{ x }{ 4 } \right) \right|$.
1. Find the Fourier series of the function.
2. Using this decomposition, calculate the sum of the series $\sum_{n=1}^\infty \frac{ (-1)^n }{ 4 \cdot n^2 - 1 }$.
3. Using this decomposition, calculate the sum of the series $\sum_{n=1}^\infty \frac{ 1 }{ 4 \cdot n^2 - 1 }$. | 1. The Fourier series is $\frac{2}{\pi}+\sum_{n=1}^\infty\left(\frac{4\cdot(-1)^n}{\pi\cdot\left(1-4\cdot n^2\right)}\cdot\cos\left(\frac{n\cdot x}{2}\right)\right)$
2. The sum of the series $\sum_{n=1}^\infty \frac{ (-1)^n }{ 4 \cdot n^2 - 1 }$ is $\frac{(2-\pi)}{4}$
3. The sum of the series $\sum_{n=1}^\infty \frac{ 1 }{ 4 \cdot n^2 - 1 }$ is $\frac{1}{2}$ |
413e37c6-98fa-4a69-b221-df34e3edf581 | precalculus_review | false | null | Solve $\cos(2 \cdot t) - 5 \cdot \sin(t) - 3 = 0$. | The final answer: $t=(-1)^{n+1}\cdot\frac{\pi}{6}+n\cdot\pi$ |
4209a5fe-b497-4040-8ef0-966c0d49f267 | multivariable_calculus | false | null | Find the center of mass of the region $\rho(x,y,z) = z$ on the inverted cone with radius $2$ and height $2$. | Center of mass: $P\left(0,0,\frac{8}{5}\right)$ |
429cab49-5ba8-46af-84cc-70f96e481e6a | algebra | false | null | Solve the following equations:
1. $-10 c = -80$
2. $n - (-6) = 12$
3. $-82 + x = -20$
4. $- \frac{ r }{ 2 } = 5$
5. $r - 3.4 = 7.1$
6. $\frac{ g }{ 2.5 } = 1.8$
7. $4.8 m = 43.2$
8. $\frac{ 3 }{ 4 } t = \frac{ 9 }{ 20 }$
9. $3\frac{ 2 }{ 3 } + m = 5\frac{ 1 }{ 6 }$ | The solutions to the given equations are:
1. $c=8$
2. $n=6$
3. $x=62$
4. $r=-10$
5. $r=10.5$
6. $g=\frac{ 9 }{ 2 }$
7. $m=9$
8. $t=\frac{3}{5}$
9. $m=\frac{3}{2}$ |
42ad9bcd-2e08-48bf-b2c5-8cbbbf1603db | integral_calc | false | null | The region bounded by the arc of the curve $y = \sqrt{2} \cdot \sin(2 \cdot x)$, $0 \le x \le \frac{ \pi }{ 2 }$, is revolved around the x-axis. Compute the surface area of this solid of revolution. | Surface Area: $\frac{\pi}{4}\cdot\left(12\cdot\sqrt{2}+\ln\left(17+12\cdot\sqrt{2}\right)\right)$ |
42c46aac-2976-4b49-a356-6d6ad55f62b2 | sequences_series | false | null | Given that $\frac{ 1 }{ 1-x } = \sum_{n=0}^\infty x^n$, use term-by-term differentiation or integration to find a power series for the function $f(x) = \frac{ 2 \cdot x }{ \left(1-x^2\right)^2 }$ centered at $x=0$. | $\frac{ 2 \cdot x }{ \left(1-x^2\right)^2 }$ = $\sum_{n=0}^\infty\left(2\cdot(n+1)\cdot x^{2\cdot n+1}\right)$ |