inclusionAI/Ring-lite-rl-data huggingface dataset:
Barbara asked the butcher for 4 1/2 pound steaks that cost $15.00/pound. She also asked for a pound and half of chicken breasts that cost a certain amount per pound. She spent $42 at the butchers. How much did the chicken breasts cost per pound?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$8}
Let $P(x)$ be a polynomial with integer coefficients satisfying $$(x^2+1)P(x-1)=(x^2-10x+26)P(x)$$ for all real numbers $x.$ Find the sum of all possible values of $P(0)$ between $1$ and $5000,$ inclusive.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5100}
Let $X$ and $Y$ be two continuous random variables, whose PDFs $f_X$ and $f_Y$ are uniform. $f_X$ and $f_Y$ may overlap. For instance, they could represent two score distributions for two tuples $x$ and $y$ in a database. What is the probability for $X$ and $Y$ of having the same value $v$ (e.g., for the tuples $x$ and $y$ of having the same score)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
3 / 4 of 1 / 2 of 2 / 5 of what number equals 759.0000000000001?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5060.000000000001}
Compute
$$
\int_{1}^{2} \frac{9x+4}{x^{5}+3x^{2}+x} \, dx.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\ln \frac{80}{23}}
In trapezoid \(ABCD\) with the lengths of the bases \(AD = 12 \text{ cm}\) and \(BC = 8 \text{ cm}\), a point \(M\) is taken on the ray \(BC\) such that \(AM\) divides the trapezoid into two equal areas. Find \(CM\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2.4 \text{ cm}}
Given the function $y=\cos(2x+ \frac {\pi}{3})$, determine the horizontal shift required to obtain this function from the graph of $y=\sin 2x$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{5\pi}{12}}
Monic quadratic polynomial $P(x)$ and $Q(x)$ have the property that $P(Q(x))$ has zeros at $x=-23, -21, -17,$ and $-15$, and $Q(P(x))$ has zeros at $x=-59,-57,-51$ and $-49$. Find the sum of the minimum values of $P(x)$ and $Q(x)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-100}
Exercise 12. Let $A B C$ be an isosceles triangle at $A$ such that $\widehat{C B A}=61^{\circ}$. Let $E$ be the point, other than $A$, located on the circumcircle of $A B C$ such that $E B=E C$. Let $D$ be the point other than $A$ such that $D B=D C=A B$.

Determine the value in degrees of the angle $\widehat{B E D}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{119}
Points $F_{1}$ and $F_{2}$ are the left and right foci of the ellipse $C$: $\frac{x^{2}}{2}+y^{2}=1$, respectively. Point $N$ is the top vertex of the ellipse $C$. If a moving point $M$ satisfies $|\overrightarrow{MN}|^{2}=2\overrightarrow{MF_{1}}\cdot\overrightarrow{MF_{2}}$, then the maximum value of $|\overrightarrow{MF_{1}}+2\overrightarrow{MF_{2}}|$ is \_\_\_\_\_\_
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6+\sqrt{10}}
A point is randomly thrown on the segment [12, 17] and let $k$ be the resulting value. Find the probability that the roots of the equation $\left(k^{2}+k-90\right) x^{2}+(3 k-8) x+2=0$ satisfy the condition $x_{1} \leq 2 x_{2}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2/3}
Find the area of a triangle if two of its sides are 1 and $\sqrt{15}$, and the median to the third side equals 1.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\sqrt{15}}{2}}
Joey the postman takes 1 hour to run a certain route every day. He delivers packages and then returns to the post office along the same path. The average speed of the round trip is 3 miles/hour, and the speed with which Joey returns is 6.000000000000002 miles/hour. How long is the route Joey runs?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1.5}
Each square on a chessboard has a knight placed on it. What is the minimum number of knights that need to be removed from the board so that there is no knight left that attacks exactly four other knights? (A knight attacks cells that are one square horizontally and two squares vertically away or vice versa.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
In a new diagram, the grid is composed of squares. The grid is segmented into various levels that step upwards as you move to the right. Determine the area of the shaded region in the following configuration:
- The grid dimensions are 15 units wide and 5 units tall.
- The shaded region fills up from the bottom to a height of 2 units for the first 4 units of width, then rises to fill up to 3 units height until the 9th unit of width, then continues up to 4 units height until the 13th unit of width, and finally fills up to 5 units height until the 15th unit of width.
- An unshaded triangle is formed on the rightmost side, with a base of 15 units along the bottom and a height of 5 units.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{37.5}
What is the probability that in a randomly chosen arrangement of the numbers and letters in "HMMT2005," one can read either "HMMT" or "2005" from left to right?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{23/144}
The 79 interns of the Animath internship each choose an activity for the free afternoon from 5 proposed activities. We know that:

- The swimming pool was at least as popular as football
- Students went shopping in groups of 5
- At most 4 students played cards
- At most one student stayed in their room

We write next to each activity the number of students who participated in it. How many different lists could we have written?

## Combinatorial identities
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\binom{81}{2}}
13.418 Two cyclists leave point $A$ simultaneously at different speeds and head for point $B$. Upon reaching it, they immediately turn back. The first cyclist, who was faster than the second, meets the second one on the return trip at a distance of $a$ km from $B$; then, after reaching $A$, he heads again towards $B$ and, having traveled $\boldsymbol{k}$-th of the distance $A B$, meets the second cyclist, who is returning from $B$. Find the distance from $\boldsymbol{A}$ to $\boldsymbol{B}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2ak}
Given $p$: $|4x-3|\leqslant 1$ and $q$: $x^{2}-(2a+1)x+a^{2}+a\leqslant 0$, find the range of values for $a$ if $p$ is a necessary but not sufficient condition for $q$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[0, \frac{1}{2}]}
Let \( A \), \( B \), and \( C \) be distinct points on the parabola \( y = x^2 \), and let \( R \) be the radius of the circumcircle of triangle \( \triangle ABC \). Determine the range of possible values for \( R \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\left(\frac{1}{2}, +\infty\right)}
$n \times n$ 矩阵 $A_{n}$ 的主对角元素为 $n$ ，其余元素为 $1$ .已知多项式 $f(x)$ 满足 $f\left(A_{n}\right)=O$对任意 $1 \leqslant n \leqslant 100$ 均成立, 则 $\operatorname{deg} f$ 的最小值为 $\qquad$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{149}
There are eight identical Black Queens in the first row of a chessboard and eight identical White Queens in the last row. The Queens move one at a time, horizontally, vertically or diagonally by any number of squares as long as no other Queens are in the way. Black and White Queens move alternately. What is the minimal number of moves required for interchanging the Black and White Queens?

[i](5 points)[/i]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{24}
A large sphere is on a horizontal field on a sunny day. At a certain time the shadow of the sphere reaches out a distance of $10$ m from the point where the sphere touches the ground. At the same instant a meter stick (held vertically with one end on the ground) casts a shadow of length $2$ m. What is the radius of the sphere in meters? (Assume the sun's rays are parallel and the meter stick is a line segment.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$10\sqrt{5}-20$}
What is the largest \( n \) for which a convex \( n \)-gon exists such that the lengths of its diagonals take no more than two different values? (I. Rubanov)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
2019 students are voting on the distribution of \( N \) items. For each item, each student submits a vote on who should receive that item, and the person with the most votes receives the item (in case of a tie, no one gets the item). Suppose that no student votes for the same person twice. Compute the maximum possible number of items one student can receive, over all possible values of \( N \) and all possible ways of voting.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1009}
We write on the board the equation

$$
(x-1)(x-2) \cdots(x-2016)=(x-1)(x-2) \cdots(x-2016),
$$

where there are 2016 linear factors on each side. What is the smallest positive value of $k$ such that we can omit exactly $k$ of these 4032 linear factors in such a way that there is at least one linear factor on each side, and the resulting equation has no real roots?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2016}
Given the approximation \( 1 - y \) for the value of \( \frac{1}{1 + y} \) where \( |y| < 1 \), find the ratio of the error made to the correct value. Express your answer as a mathematical expression.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{y^2}
设集合 $A=\left\{n \left\lvert\, \frac{n}{3} \in \mathbf{N}_{+}\right.\right\}, B=\left\{y \mid y=x+4+\sqrt{5-x^{2}}\right\}$ ，求集合 $A \bigcap B$ 中元素的个数。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
8 个女孩与 25 个男孩围成一圈，任何两个女孩之间至少站两个男孩，那么，共有多少种不同的排列方法？标准答案形式为$\frac{a!\cdot b!}{c!}$，计算出a+b+c的值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{50}
A five-digit positive integer $abcde_{10}$ ($a \neq 0$) is said to be a *range* if its digits satisfy the inequalities $a < b > c < d > e$. For example, $37452$ is a range. How many ranges are there?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8622}
Given the expansion of $(x- \frac{a}{x})^8$, the constant term is $1120$, where $a$ is a constant real number. Find the sum of the coefficients of the terms in the expansion.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6561}
Write the numbers $0, 1, 2, 3, 4, 5, 6, 7$ on the eight vertices of a cube (each vertex has one number, and all numbers must be used once), such that the sum of the two numbers on each edge is a prime number. Then, find the maximum sum of the four numbers on one face of the cube.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
Define a common chord between two intersecting circles as the line segment connecting their two intersection points. Let $\omega_1, \omega_2, \omega_3$ be three circles with radii $3, 5,$ and $7$, respectively. Suppose they are arranged such that:

1. The common chord of $\omega_1$ and $\omega_2$ is a diameter of $\omega_1$.
2. The common chord of $\omega_1$ and $\omega_3$ is a diameter of $\omega_1$.
3. The common chord of $\omega_2$ and $\omega_3$ is a diameter of $\omega_2$.

Compute the square of the area of the triangle formed by the centers of the three circles.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{96}
Inside an isosceles triangle \( ABC \) (\( AB = AC \)), a point \( K \) is marked. Point \( L \) is the midpoint of segment \( BK \). It turns out that \(\angle AKB = \angle ALC = 90^\circ \), and \( AK = CL \). Find the angles of triangle \( ABC \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{60^\circ}
Given propositions p and q, where proposition p states that the inequality $x^2 + ax - 2 > 0$ holds true for all $x$ in the interval $[1, 2]$; proposition q states that the function $f(x) = \log_{\frac{1}{3}}(x^2 - 2ax + 3a)$ is a decreasing function on the interval $[1, +\infty)$. If the proposition "p OR q" is true, determine the range of values for the real number $a$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{a > -1}
John had a stock of 1200 books in his bookshop. On Monday, he sold 75 books and had 6 books returned, on Tuesday he sold 50 books at a 20% discount, on Wednesday he sold 64 books and had 8 books returned, on Thursday he sold 78 books at a 10% discount, and on Friday he sold 135 books and had 5 books returned. What percentage of the books were not sold?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{68.08\%}
The cities A and B are located upstream and downstream of a river, respectively. Every day, a boat departs from each city at a fixed time and travels at a constant speed. Usually, they meet at 11:00 AM during their journey. One day, the boat from city B was delayed by 40 minutes, and as a result, the two boats met at 11:15 AM during their journey. It is known that the speed of the boat departing from city A in still water is 44 kilometers per hour, and the speed of the boat departing from city B in still water is the square of the uniform speed $V$ of the water flow in kilometers per hour. Find $V$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Given the parabola $C:y^{2}=2px\left(p \gt 0\right)$ with the focus at $F$, two points $A$ and $B$ on the parabola are in the first quadrant, and satisfy $|AF|=3$, $|BF|=7$, $|AB|=5$. Find the slope of the line $AB$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{3}{4}}
Cubes with each side one inch long are glued together to form a larger cube. Two adjacent faces of the larger cube are painted with red color while the remaining four adjacent faces are painted with blue color. The entire assembly is then taken apart. 24 small cubes are found with no paints on them. How many unit cubes have at least one face that is painted red, one face that is painted blue, or both red and blue faces?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{101}
For real numbers $x$ and $y$, define $x \spadesuit y = (x+y)(x-y)$. What is $3 \spadesuit (4 \spadesuit 5)$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-72}
Calculate $\sum_{i=0}^{\lfloor n / 3\rfloor}\binom{n}{3 i}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{2^{n}+2\cosn\pi/3}{3}}
设 $z_{1}, z_{2}$ 都是复数, 且 $\left|z_{1}\right|=3,\left|z_{2}\right|=5\left|z_{1}+z_{2}\right|=7$, 则 $\arg \left(\frac{z_{2}}{z_{1}}\right)^{3}$ 的值是 $\qquad$. 请给出原始答案中\pi前的常数部分值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
In \(\mathbb{R}^3\), a sphere has a diameter \(d\). What is the most probable length of random secants (including tangents, where the length is 0) drawn through the sphere?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{d}
Calculate the number of distinct paths a knight can take to move from the top-left corner to the bottom-right corner of an 8 × 8 chessboard, using only L-shaped moves.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{108}
What is the specific term for a monoid of the form $eSe$, where $e$ is an idempotent element in a semigroup $S$, similar to a "corner ring" in ring theory?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{local submonoid}
Determine the value of $a$ such that the function \( f: \mathbb{R}^2 \to \mathbb{R} \) defined by
\[
f(x,y) = \begin{cases} 
\dfrac{x\sin^{2}(x)+axy^{2}}{x^{2}+2y^{2}+3y^{4}}, & (x,y) \neq (0,0) \\
0, & (x,y) = (0,0) 
\end{cases}
\]
is differentiable at the point \((0,0)\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Find the maximum degree of a polynomial \( f \in \mathbb{Z}[x] \) such that \( |f(x)| \le 2^x \) for all \( x \in \mathbb{N} \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
Determine the covariance function \( \text{Cov}(Y(t), Y(s)) \) for the process \( Y(t) = X^2(t) \), where \( X(t) \) is a Brownian motion with variance parameter \( \sigma^2 \) for \( t \geq 0 \) and \( E(Y(t)) = t \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2 (\min(t, s))^2}
Given the equations \( xw^3 + yz^2 + z^3 = -1 \) and \( zw^3 - xz^3 + y^2w = 1 \), where \( z \) and \( w \) are differentiable functions of \( x \) and \( y \), find \( \frac{\partial z}{\partial x} \) at the point \((x, y, z, w) = (1, -1, -1, 1)\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\dfrac{5}{4}}
Let \( \vec{v} = \vec{i} \times (\vec{j} \times (\vec{k} \times (\vec{i} \times (\vec{j} \times (\vec{k} \times (\vec{i} \times (\vec{j} \times (\vec{j} \times \vec{k})))))))) \). Find the value of \( ||\vec{v}|| \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
A sealed bottle, which contains water, has been constructed by attaching a cylinder of radius \(1 \text{ cm}\) to a cylinder of radius \(3 \text{ cm}\). When the bottle is right side up, the height of the water inside is \(20 \text{ cm}\). When the bottle is upside down, the height of the liquid is \(28 \text{ cm}\). What is the total height, in \(\text{cm}\), of the bottle?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{29}
Given the vectors $\boldsymbol{a}=(0,1)$, $\boldsymbol{b}=\left(-\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$, and $\boldsymbol{c}=\left(\frac{\sqrt{3}}{2},-\frac{1}{2}\right)$. Real numbers $x, y, z$ satisfy $x \boldsymbol{a}+y \boldsymbol{b}+z \boldsymbol{c}=(1,2)$. Find the minimum value of $x^{2}+y^{2}+z^{2}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{10}{3}}
Donggyu wants to complete the diagram so that each box contains a positive integer and each box in the top two rows contains the product of the integers in the two boxes below it. He wants the integer in the top box to be 720. How many different values can the integer n take? Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
已知 A=(a_{ij})_{5\times5} 满足 a_{ij}=\df{1}{\min\{i,j\}} (1\leq i,j\leq 5)，则 [|\det A^{-1}|]=__________.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2880}
Given the hyperbola $$E: \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 (a > 0, b > 0)$$ with left and right vertices A and B, respectively. Let M be a point on the hyperbola such that ∆ABM is an isosceles triangle, and the area of its circumcircle is 4πa², then the eccentricity of the hyperbola E is _____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{2}}
If the function $f(x)=x^{2}- \frac {1}{2}\ln x+1$ is not monotonic in a subinterval $(k-1,k+1)$ of its domain, then the range of the real number $k$ is \_\_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{[1, \frac {3}{2})}
Hapi, the god of the annual flooding of the Nile, is preparing for this year's flooding. The shape of the channel of the Nile can be described by the function $y = \frac{-1000}{x^2+100}$, where the $x$ and $y$ coordinates are in meters. The current depth of the river is $5$ meters. Hapi plans to increase the water level by $3$ meters. How many meters wide will the river be after the flooding? The depth of the river is always measured at its deepest point.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{40}
In a village in Sri Lanka, 10% of the population died during the first bombardment. Following that, another 5% of the remaining population died during a second bombardment. After these two tragic events, 15% of the surviving population left the village on account of fear. Concurrently, an influx of refugees from neighboring areas increased the village population by 8%. If, after all these occurrences, the population is reduced to 6514, how much was it in the beginning?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8300}
Consider the number $99,\!999,\!999,\!999$ squared. Following a pattern observed in previous problems, determine how many zeros are in the decimal expansion of this number squared.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
Let $S_{7}$ denote all the permutations of $1,2, \ldots, 7$. For any \pi \in S_{7}$, let $f(\pi)$ be the smallest positive integer $i$ such that \pi(1), \pi(2), \ldots, \pi(i)$ is a permutation of $1,2, \ldots, i$. Compute \sum_{\pi \in S_{7}} f(\pi)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{29093}
Xiaoming, a primary school student, asked his grandfather how old he was this year. His grandfather replied, "This year, my age is more than 7 times yours. In a few years, it will become 6 times yours, then 5 times after a few more years, and eventually 4 times after some years. Can you guess how old I am this year?" After some calculations, Xiaoming finally figured out that his grandfather is     years old this year.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{69}
A towel, after being bleached, was found to have different rates of shrinkage - it lost 20% of its original length, and 10% of its original breadth. Also, due to a specific characteristic of the material used, a cumulative shrinkage occurred amounting to a reduction of 5% in overall size. Additionally, after the bleaching process, the towels are folded in half, resulting in further changes to the observable surface area. Determine the percentage change in the observable surface area of the towel after the bleaching process and subsequent folding.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{65.8\%}
What is $\lim_{x\to 0^+} \int_0^\infty \frac{e^{-xt}}{\sqrt{t^2 +t}} dt$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{+\infty}
On a large piece of paper, Dana creates a "rectangular spiral" by drawing line segments of lengths, in cm, of 1, 1, 2, 2, 3, 3, 4, 4, ... as shown. Dana's pen runs out of ink after the total of all the lengths he has drawn is 3000 cm. What is the length of the longest line segment that Dana draws, in cm?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{54}
Given triangle $\triangle ABC$, $A=120^{\circ}$, $D$ is a point on side $BC$, $AD\bot AC$, and $AD=2$. Calculate the possible area of $\triangle ABC$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{8\sqrt{3}}{3}}
Square $EFGH$ has sides of length 4. Segments $EK$ and $EL$ divide the square's area into two equal parts. Calculate the length of segment $EK$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4\sqrt{2}}
Find the limit $$\lim_{x\to2}\frac{\sqrt[4]{x}-\sqrt[4]{2}}{\sqrt[3]{x}-\sqrt[3]{2}}$$ without using L'Hopital's rule. Can you express the limit in a simplified form without resorting to derivatives?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\(\frac{3}{4 \sqrt[12]{2}}\)}