inclusionAI/Ring-lite-rl-data huggingface dataset:
Five positive integers (not necessarily all different) are written on five cards. The sum of the numbers on every pair of cards is calculated, and only three different totals are obtained: 57, 70, and 83. Find the largest integer on any card. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{48}
Find the largest positive integer \( n \), such that there exists a set with \( n \) elements where exactly 1 element is divisible by \( n \), exactly 2 elements are divisible by \( n-1 \), ..., exactly \( n-1 \) elements are divisible by 2, and \( n \) elements are divisible by 1.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
For a positive integer \( n \), let \( \varphi(n) \) denote the number of positive integers less than or equal to \( n \) that are coprime to \( n \). Let \( f(n) \) denote the smallest positive integer greater than \( n \) that is not coprime to \( n \). If \( f(n) = m \) and \( \varphi(m) = n \), then the pair of positive integers \( (n, m) \) is called a friendly pair. Find all friendly pairs.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(2, 4)}
Two ants sit at the vertex of the parabola $y = x^2$.  One starts walking northeast (i.e., upward along the line $y = x$ and the other starts walking northwest (i.e., upward along the line $y = -x$).  Each time they reach the parabola again, they swap directions and continue walking.  Both ants walk at the same speed.  When the ants meet for the eleventh time (including the time at the origin), their paths will enclose 10 squares.  What is the total area of these squares?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{770}
In order to obtain an income of Rs. 500 from a certain percentage stock at Rs. 90, one must make an investment of Rs. 1500. What is the percentage of the stock?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30\%}
Problem 3. A clock shows exactly one o'clock. A mosquito and a fly are sitting at the same distance from the center on the hour and minute hands, respectively. When the hands coincide, the insects swap places. How many times greater is the distance that the mosquito has traveled in half a day compared to the distance the fly has traveled in the same time?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{83}{73}}
Simplify the expression \( \left( 7 + 4 \sqrt{3} ight)^{\frac{1}{2}} - \left( 7 - 4 \sqrt{3} ight)^{\frac{1}{2}} \) and express your answer as a simplified expression involving square roots.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 \sqrt{3}}
You are given a rectangular playing field of size $13 \times 2$ and any number of dominoes of sizes $2 \times 1$ and $3 \times 1$. The playing field should be completely covered with these dominoes without any overlaps, and no domino should protrude beyond the playing field. Furthermore, all dominoes must be aligned in the same direction, meaning their longer sides must be parallel to each other. How many such coverings are possible?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{257}
In a group of 8 boys and 6 girls, a committee of 8 persons is to be formed. The committee must have an equal number of boys and girls and at least two members under the age of 18. Additionally, at least one girl must have experience in leadership and one boy must have experience in event planning. In how many different ways can the committee be formed under these conditions?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{350}
What is the maximum number of months in a year that can have five Sundays?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Anya, Borya, and Vasya took the same 6-question test, where each question could be answered with "yes" or "no". The answers are shown in the table:

| Question # | 1 | 2 | 3 | 4 | 5 | 6 |
| :--- | :--- | :--- | :--- | :--- | :--- | :--- |
| Anya | no | yes | no | yes | no | yes |
| Borya | no | no | yes | yes | no | yes |
| Vasya | yes | no | no | no | yes | no |

It turned out that Anya had two incorrect answers, and Borya had only two correct answers. How many incorrect answers does Vasya have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
设$x ^ { 2 } + y ^ { 2 } - 2 x - 2 y + 1 = 0 ( x , y \in R )$，则$F ( x , y ) = \frac { x + 1 } { y }$的最小值为
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$\frac { 3 } { 4 }$}
In a convex quadrilateral $ABCD$, it is given that $\angle BAD = \angle BCD = 90^\circ$ and $BC = CD$. Let $E$ be the intersection of diagonals $\overline{AC}$ and $\overline{BD}$. Given that $\angle AED = 123^\circ$, find the degree measure of $\angle ABD$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{78}
Define $a_k = 2^{2^{k-2013}} + k$ for all integers $k$. Simplify the expression:

$$(a_0 + a_1)(a_1 - a_0)(a_2 - a_1)\cdots(a_{2013} - a_{2012}).$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Given a sequence $\{a_n\}$ with the sum of its first $n$ terms denoted as $S_n$, if $S_n$, $S_{n-1}$, and $S_{n+1}$ (for $n \geqslant 2$) form an arithmetic sequence, and $a_2 = -2$, then $a_4 =$ ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-8}
The line $ax+my-2a=0$ ($m \neq 0$) passes through the point $(1,1)$. The angle of inclination of this line is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{135^{\circ}}
In each cell of a $5 \times 5$ board, there is either an X or an O, and no three Xs are consecutive horizontally, vertically, or diagonally. What is the maximum number of Xs that can be on the board?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{16}
## Task A-4.5. (4 points)

A rectangular path with a width of $1.5 \mathrm{~m}$ and a length of $20 \mathrm{~m}$ needs to be tiled with identical tiles in the shape of an isosceles right triangle with legs of length $50 \mathrm{~cm}$, such that the legs are parallel to the sides of the rectangle. Determine the number of ways this can be done.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{120}}
Alice's white water rafting event is composed of 40 students and 10 instructors, including herself, in her class. In total, there are 4 classes participating in the event. Each student has a 40% probability of bringing their own life vest. How many more life vests will Alice need to get so that everyone attending the event has one?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{136}
Let $a = -\sqrt{3} + \sqrt{5} + \sqrt{7}$, $b = \sqrt{3} - \sqrt{5} + \sqrt{7}$, $c = \sqrt{3} + \sqrt{5} - \sqrt{7}$. Evaluate the expression:
\[
\frac{a^4}{(a-b)(a-c)} + \frac{b^4}{(b-c)(b-a)} + \frac{c^4}{(c-a)(c-b)}.
\]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{30}
Given complex numbers \( x \) and \( y \), find the maximum value of \(\frac{|3x+4y|}{\sqrt{|x|^{2} + |y|^{2} + \left|x^{2}+y^{2}\right|}}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{5\sqrt{2}}{2}}
Find the value of the ratio $\frac{I_1}{I_2}$, where $I_1=\int_{0}^{1} \frac{\tan^{-1}x}{x} dx$ and $I_2=\int_{0}^{\pi/2} \frac{x}{\sin x}dx$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1/2}
Eve randomly chooses two **distinct** points on the coordinate plane from the set of all $11^2$ lattice points $(x, y)$ with $0 \le x \le 10$, $0 \le y \le 10$. Then, Anne the ant walks from the point $(0,0)$ to the point $(10, 10)$ using a sequence of one-unit right steps and one-unit up steps. Let $P$ be the number of paths Anne could take that pass through both of the points that Eve chose. The expected value of $P$ is $\binom{20}{10} \cdot \frac{a}{b}$ for relatively prime positive integers $a$ and $b$. Compute $100a+b$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{942}
Circles \(\omega_{1}\) and \(\omega_{2}\) intersect at points \(A\) and \(B\), and a circle centered at point \(O\) encompasses circles \(\omega_{1}\) and \(\omega_{2}\), touching them at points \(C\) and \(D\) respectively. It turns out that points \(A, C\), and \(D\) are collinear. Find the angle \(\angle ABO\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{90^\circ}
An inverted frustum with a bottom diameter of 12 and height of 18, filled with water, is emptied into another cylindrical container with a bottom diameter of 24. Assuming the cylindrical container is sufficiently tall, calculate the height of the water level in the cylindrical container. Express your answer as a decimal value with one digit after the decimal point.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1.5}
在 $(x+y+z)^{8}$ 的展开式中，求所有形如 $x^{2} y^{a} z^{b}(a, b \in \mathbf{N})$ 的项的系数之和。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1792}
James can buy a new computer for $600 and have it last a certain number of years, or buy 2 used computers for $200 each that each last 3 years. He will save $200 by picking the cheaper option. How long will the new computer last?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Baron Munchausen told a story. "There were a whole crowd of us. We reached a crossroads. Then half of our group turned left, a third turned right, and a fifth went straight." "But wait, the Duke remarked, the sum of half, a third, and a fifth isn't equal to one, so you are lying!" The Baron replied, "I'm not lying, I'm rounding. For example, there are 17 people. I say that a third turned. Should one person split in your opinion? No, with rounding, six people turned. From whole numbers, the closest to the fraction $17 / 3$ is 6. And if I say that half of the 17 people turned, it means 8 or 9 people." It is known that Baron Munchausen never lies. What is the largest number of people that could have been in the crowd?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{37}
If the equation $9^x + a \cdot 3^x + 4 = 0$ has a solution, then the range of the real number $a$ is \_\_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(-\infty, -4]}
Let \( m, n > 2 \) be integers. One of the angles of a regular \( n \)-gon is dissected into \( m \) angles of equal size by \( (m-1) \) rays. If each of these rays intersects the polygon again at one of its vertices, we say \( n \) is \( m \)-cut. Compute the smallest positive integer \( n \) that is both 3-cut and 4-cut.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14}
Let $x=\sqrt{37-20\sqrt{3}}$. Find the value of \(\frac{x^4-9x^3+5x^2-7x+68}{x^2-10x+19}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Brian goes fishing twice as often as Chris, but catches 2/5 times fewer fish than Chris per trip. If Brian caught 400 fish every time he went fishing, how many fish did they catch altogether if Chris went fishing 10 times?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13600}
Given the function $f(x) = 1 + x - \frac{x^2}{2} + \frac{x^3}{3} - \frac{x^4}{4} + \ldots + \frac{x^{2013}}{2013}$, and $g(x) = 1 - x + \frac{x^2}{2} - \frac{x^3}{3} + \frac{x^4}{4} + \ldots - \frac{x^{2013}}{2013}$. Let $F(x) = f(x+3)g(x-4)$ and all zeros of $F(x)$ are within the interval $[a, b]$ ($a < b$, $a, b \in \mathbb{Z}$). The minimum value of $b-a$ is \_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
2. Dan is holding one end of a 26 inch long piece of light string that has a heavy bead on it with each hand (so that the string lies along straight lines). If he starts with his hands together at the start and leaves his hands at the same height, how far does he need to pull his hands apart so that the bead moves upward by 8 inches?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24}
What is the smallest number of kings that must be taken so that, after being placed arbitrarily on an $8 \times 8$ chessboard, there will necessarily be two kings attacking the same square?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
If $x$, $y$, and $z$ are real numbers such that $x^2 + z^2 = 1$ and $y^2 + 2y(x + z) = 6$, find the maximum value of $y(z - x)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
函数 $f(x)=\frac{\sqrt{2}}{2}(\cos x-\sin x) \sin \left(x+\frac{\pi}{4}\right)-2 a \sin x+b(a>0)$ 的最大值为 1, 最小值为 -4, 求 $b$ 的值.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-1}
An isosceles triangle with a base equal to \(a\) has an inscribed circle, and three tangents are drawn to it such that they cut off three smaller triangles from the given triangle. The sum of the perimeters of these smaller triangles is \(b\). Find the side length of the given isosceles triangle.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{b - a}{2}}
Let \( A = \{1, 2, 3, \cdots, 4n+2\} \) and \( M = \{2n+1, 4n+3, 6n+5\} \). For any non-empty subset \( B \) of \( A \), \( B \) is called an \( M \)-free set if the sum of any two numbers in \( B \) does not belong to \( M \). If \( A = A_1 \cup A_2 \), \( A_1 \cap A_2 = \varnothing \), and both \( A_1 \) and \( A_2 \) are \( M \)-free sets, then the ordered pair \( (A_1, A_2) \) is called an \( M \)-partition of \( A \). Find the number of all \( M \)-partitions of \( A \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{n+1}}
In triangle \(ABC\), the median \(AD\) and the angle bisector \(BE\) are perpendicular and intersect at point \(F\). It is known that \(S_{DEF} = 5\). Find \(S_{ABC}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60}
A box contains 5 white balls and 6 black balls. I draw them out of the box, one at a time. What is the probability that all of my draws alternate in color starting with a black ball?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{462}}
454. Several identical boxes together weigh 10 tons, with each of them weighing no more than 1 ton. What is the minimum number of three-ton trucks needed to haul away all this cargo in one trip?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
There is a rectangular prism made of 1 in cubes that has been covered in tin foil. There are exactly 128 cubes that are not touching any tin foil on any of their sides. If the width of the figure created by these 128 cubes is twice the length and twice the height, what is the measure m in inches of the width of the foil covered prism?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
The union of sets $A$ and $B$ is $A \cup B = \left\{a_{1}, a_{2}, a_{3}\right\}$. When $A \neq B$, the pairs $(A, B)$ and $(B, A)$ are considered different. How many such pairs $(A, B)$ are there?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{27}
Fifteen students numbered $1, 2, 3, \ldots, 15$ stand in a circle facing inward. On the first turn, the student with number 1 turns around to face outward. On the second turn, the students numbered 2 and 3 turn around. On the third turn, the students numbered $4, 5, 6$ turn around, and so on. On the 15th turn, all students turn around. After the 12th turn, how many students are still facing outward?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
Determine the Löwenheim number of the extended first-order logic $L(Q^c)$, which includes Chang's quantifier $Q^c$. What is this Löwenheim number?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\aleph_1}
Thirty people are seated at three round tables, each with ten seats, at an alumni dinner. After each time interval \( \Delta t \), everyone changes position simultaneously to sit next to different people on their left and right. What is the minimum number of seating configurations required for everyone to have sat next to every other person at least once? If it is not possible for everyone to sit next to each other just once, specify the minimum number of configurations needed for everyone to sit next to each other at least once.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{15}
Suppose $n$ has at least two distinct odd prime factors. If $x^2 \equiv y^2 \pmod{n}$ and $\gcd(x,y) = 1$, find the probability that $\gcd(n, x-y)$ is a non-trivial factor of $n$. Express your answer as a fraction.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{1}{2}}
An urn contains 18 black balls and 2 white balls. What is the expected number of draws (without replacement) needed to obtain two balls of different colors?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\dfrac{135}{19}}
Find the envelope of the family of straight lines given by the equation \( x \cos \alpha + y \sin \alpha = a \sec \alpha \), where \( \alpha \) is a parameter.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{y^2 = 4a(a - x)}
Find the volume of the solid formed by the intersection of three cylinders, each with a length of 1 unit along the x, y, and z axes, starting from the origin, and each having a radius of 1 unit.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 - \sqrt{2}}
Given a set of sentences \(\Sigma = \{\gamma_{\geq n} : n\) is even\}, where \(\gamma_{\geq n}\) is a sentence such that its models have the cardinality of at least \(n\), determine the smallest model of \(\Sigma\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\aleph_0}
In a game played inside the unit disc $\mathcal{D}$, player $\mathcal{A}$ chooses a point $p_0 \in \mathcal{D}$. At each step $n$, player $\mathcal{B}$ draws a line $\ell_n$ through $p_{n-1}$, and $\mathcal{A}$ chooses a point $p_n \in \mathcal{D} \cap \ell_n$. Player $\mathcal{B}$ wins if they can force the sequence $(p_n)$ to converge; otherwise, $\mathcal{A}$ wins. If both players play randomly, what is the probability that $\mathcal{B}$ wins?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Suppose $\{A_{1},...,A_{k}\}$ is a set of linearly independent elements in an irreducible $\mathbb{R}$-algebra $D$ in $M_{n}(\mathbb{C})$. If $D$ is isomorphic to $\mathbb{H}$ and has dimension $4$ as an $\mathbb{R}$-algebra, find the value of $k$. \(\boxed{}\)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Determine the limits of integration for the radial coordinate $r$ when using the divergence theorem to evaluate the surface integral \( I = \int \int F \cdot n \, dS \) where \( F = x^3 i + y^3 j + z^3 k \) and \( S \) is the surface of the cylinder \( x^2 + y^2 = 4 \) between \( -1 < z < 1 \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[0, 2]}
Calculate the volume of a regular triangular pyramid where the midpoint of its height is 2 units away from a lateral face and \(\sqrt{12}\) units away from a lateral edge. Round your answer to two decimal places if necessary.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{374.12}
Given the functions \( f(x) = 3xe^{-x} \) and \( g(x) = \frac{x}{2} \), let \( v \) be the x-coordinate of their second intersection point (not 0). Find the value of \( u \), where \( 0 < u < v \), such that the area of the triangle with vertices \([0, 0], [u, f(u)], [u, g(u)]\) is maximized.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1.049}
Find a function of a natural number \( M \) that yields an odd square, such as 9 or 25, only when \( M \) is a triangular number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8M + 1}
Let $K(O,R)$ be a circle with center $O$ and radious $R$ and $(e)$ to be a line thst tangent to $K$ at $A$. A line parallel to $OA$ cuts $K$ at $B, C$, and $(e)$ at $D$, ($C$ is between $B$ and $D$). Let $E$ to be the antidiameric of $C$ with respect to $K$. $EA$ cuts $BD$ at $F$.
If $R=\frac{5}{2}, AD=\frac{3}{2}$, calculate the area of $EBF$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13.5}
Evaluate the improper integral: $$\int_{0}^{\infty} \left(e^{-\frac{1}{x^2}}-e^{-\frac{4}{x^2}}\right) dx$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{\pi}}
An egg plant is a hollow cylinder of negligible thickness with radius $2$ and height $h$. Inside the egg plant, there is enough space for four solid spherical eggs of radius $1$. What is the minimum possible value for $h$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
When the celebrated German mathematician Karl Gauss (1777-1855) was nine years old, he was asked to add all the integers from 1 through 100. He quickly added 1 and 100, 2 and 99, and so on for 50 pairs of numbers each adding in 101. His answer was 50 · 101=5,050. Now find the sum of all the digits in the integers from 1 through 1,000,000 (i.e. all the digits in those numbers, not the numbers themselves).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{27,000,001

}
Find the smallest cardinality multiset \( x \) such that every element of the set \( z = \{ 1, 5, 6, 10, 11, 35, 36 \} \) can be expressed as a sum of elements from \( x \). For example, one possible multiset is \( x = \{1, 5, 5, 30\} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Find the minimum value of the expression \(\frac{5x^{2}+8xy+5y^{2}-14x-10y+30}{(4-x^{2}-10xy-25y^{2})^{7/2}}\). Round your answer to the nearest hundredth if necessary.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.16}
Determine the number of natural numbers \( n \) in the interval \([1005, 2010]\) for which the polynomial \(1 + x + x^2 + \cdots + x^{n-1}\) divides the polynomial \(1 + x^2 + x^4 + \cdots + x^{2010}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
Given the function $f : \mathbb{Z}_{\geq 0} \to \mathbb{Z}_{\geq 0}$ satisfying $f(1)=1$ and the functional equation \[ f\left(f(x+1) + f\left( x + f(x)\right)\right) = x+2, \] determine the value of $f(10)$. 
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
Find a value $p > 1$ such that the series $\sum_n f_n$ converges in $L^p(\mathbb{R})$, where the functions are defined as:
$$ f_n(x) = \frac{1}{1 + n^2\sqrt{x}}\chi_{[\exp(2n), 2\exp(2n+2)]} $$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Determine the distribution of the sum of the squares of two independent random variables, each following a standard normal distribution \(N(0, 1)\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\chi^2(2)}
Determine the number of different solutions to the equation \(x^2_{1}+2x^2_{2}+3x^3_{3}=4x^2_{4}\) over the field with 7 elements, \(\mathbb{F}_{7}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{343}