inclusionAI/Ring-lite-rl-data huggingface dataset:
Simplify the following propositional logic expression to the form with the least atomic propositions:

$$\lnot ((P \Rightarrow (Q \Rightarrow R)) \Rightarrow (Q \Rightarrow (P \Rightarrow R)))$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\bot}
Mark Watney tests the durability of a new dome designed for the Mars expedition. The dome is in the shape of a hemisphere with a radius of 20 meters. Mark turns to the north and shoots at an angle of $45^{\circ}$ to the ground, then turns to the south and also shoots at an angle of $45^{\circ}$ (see figure). What values can $\left|P_{1} P_{2}\right|$ - the distance between the points of impact, take?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20\sqrt{2}}
Given a grid formed by $n$ horizontal lines and $n$ vertical lines, how many distinct closed paths with $2n$ segments can be drawn such that each path passes through each horizontal line and each vertical line exactly once?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{n! \cdot (n-1)!}{2}}
Given that the original value of the house is $12000, Mr. A sells it at a 15% loss, and then Mr. B sells it back to Mr. A at a 20% gain after holding it for one year and accruing a 5% annual interest, calculate the total amount Mr. A spends to buy back the house including the interest accrued.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12852}
A quadrilateral $ABCD$ is inscribed in a circle. Suppose that $|DA| =|BC|= 2$ and$ |AB|  = 4$. Let $E $ be the intersection  point of lines $BC$ and $DA$. Suppose that $\angle AEB = 60^o$ and that $|CD| <|AB|$. Calculate the radius of the circle.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
Inside a right circular cone with base radius $5$ and height $12$ are three congruent spheres with radius $r$. Each sphere is tangent to the other two spheres and also tangent to the base and side of the cone. What is $r$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$\frac{90-40\sqrt{3}}{11}$}
Given the function f(x)=sin(ωx+φ) (ω>0, |φ|≤π/2), x=-π/4 is a zero point of f(x), x=π/4 is the symmetric axis of the graph of y=f(x), and f(x) is monotonic in (π/18, 5π/36), find the maximum value of ω.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{9}
Given that $S$, $A$, $B$, $C$ are distinct points on the surface of a sphere $O$, $SA \perp$ plane $ABC$, $AB \perp BC$, $AB=1$, $BC= \sqrt{2}$, and the surface area of sphere $O$ is $4\pi$, calculate the value of $SA$. Express your answer as a single number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
For how many ordered triples $(x,y,z)$ of nonnegative integers less than $20$ are there exactly two distinct elements in the set $\{i^x, (1+i)^y, z\}$, where $i=\sqrt{-1}$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{225}
The line $x+ay=3$ is tangent to the circle $(x-1)^{2}+y^{2}=2$. Find the value of $a$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\pm1}
In a certain kingdom, there were 32 knights. Some of them were vassals of others (a vassal could have only one suzerain, and a suzerain was always richer than his vassal). A knight who had at least four vassals bore the title of baron. What is the maximum number of barons that could be under these conditions?

(The kingdom had a law: "a vassal of my vassal is not my vassal".)

#
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7}
A  $3$  by  $3$  determinant has three entries equal to  $2$ , three entries equal to  $5$ , and three entries equal to  $8$ . Find the maximum possible value of the determinant.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{405}
Determine the number of distinct ways to express 1,000,000 as a product of three natural numbers, where products that differ only in the order of the factors are considered identical.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{139}
A sphere is circumscribed around a tetrahedron \(ABCD\). Another sphere with radius 1 is tangent to plane \(ABC\), and both spheres are internally tangent at point \(D\). Given \(AD = 3\), \(\cos \angle BAC = \frac{4}{5}\), and \(\cos \angle BAD = \cos \angle CAD = \frac{1}{\sqrt{2}}\), find the volume of the tetrahedron \(ABCD\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{18}{5}}
Let $A$ be a subset of $\{1, 2, \dots , 1000000\}$ such that for any $x, y \in A$ with $x \neq y$, we have $xy \notin A$. Determine the maximum possible size of $A$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{999001}
Pyramid $EARLY$ has rectangular base $EARL$ and apex $Y$, and all of its edges are of integer length. The four edges from the apex have lengths $1, 4, 7, 8$ (in no particular order), and EY is perpendicular to $YR$. Find the area of rectangle $EARL$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{28}
A man can row a boat at 15 kmph in still water. If he rows downstream, where the speed of current is 3 kmph, he takes 17.998560115190784 seconds to cover a certain distance. What is the distance he covers?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{89.99}
设三次函数$f ( x ) = a x ^ { 3 } + b x ^ { 2 } + c x + d ( a \neq 0 )$在区间$［0,1］$上，其值的绝对值均不大于1，求$|a|+|b|+|c|+|d|$的最大值.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{99}
Solve the equation \(\sqrt{4 x^{2}+2 x+1}-\sqrt{4 x^{2}+14 x+5}=6 x+2\) and determine the number of real roots. Express your answer as a single integer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
Arrange the digits \(1, 2, 3, 4, 5, 6, 7, 8, 9\) in some order to form a nine-digit number \(\overline{\text{abcdefghi}}\). If \(A = \overline{\text{abc}} + \overline{\text{bcd}} + \overline{\text{cde}} + \overline{\text{def}} + \overline{\text{efg}} + \overline{\text{fgh}} + \overline{\text{ghi}}\), find the maximum possible value of \(A\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4648}
An octagon is inscribed in a square so that the vertices of the octagon trisect the sides of the square. The perimeter of the square is 108 centimeters. What is the number of square centimeters in the area of the octagon?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{567}
Consider the piecewise constant interpolation of the function $f(x) = ln(x)$ , $10 ≤ x ≤ 11$ , at points $x_i = 10+ih$, where $h = 0.1$. Thus, our interpolant satisfies $v(x) = ln(10+ih)$, $10 + ih − 0.5h ≤ x < 10 + ih + 0.5h$, for $i = 0, 1, . . . , 11$. Find a bound for the error in this interpolation, i.e. find a (reasonably small) constant M such that $|f(x) − v(x)| < M$ for any $10 ≤ x ≤ 11$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0.005}
Find the cost of fencing around a circular field of diameter 20 m at the rate of Rs. 1.50 a meter. What is the total cost of fencing?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{94.25}
Cary starts working at Game Stop for $10/hour. In the first year, she works 40 hours a week for 50 weeks, with 2 weeks of vacation. After this year, she gets a 20% raise. Additionally, she earns a performance bonus of $500 at the end of the year. 

In the second year, her base pay is cut to 75% of what it used to be due to the company's profits decreasing, but she is now working an average of 50 hours per week, where hours beyond 40 are paid at 1.5 times the normal rate. She takes only 1 week of vacation in the second year. Moreover, she incurs a $300 penalty for underperformance in the second year.

In the third year, she receives another 10% raise of her base pay, almost back to her original starting wage, and her hours go back to 40 hours a week with 2 weeks of vacation. Also, she earns a performance bonus of $1,000 at the end of the third year.

Throughout these three years, the income tax rates change: in the first year, it is 20%; in the second year, 22%; and in the third year, it is 18%. Calculate Cary's total net earnings, after taxes and accounting for bonuses and penalties, over these three years.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$52,913.10}
Simplify the expression \(\frac{\log _{a} \sqrt{a^{2}-1} \cdot \log _{1 / a}^{2} \sqrt{a^{2}-1}}{\log _{a^{2}}\left(a^{2}-1\right) \cdot \log _{\sqrt[3]{a}} \sqrt[6]{a^{2}-1}}\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\log _{a} \sqrt{a^{2}-1}}
Given that \(b\) and \(c\) are both integers and \(c < 2000\). If the quadratic equation \(x^{2} - bx + c = 0\) has roots whose real parts are both greater than 1, how many pairs \((b, c)\) satisfy this condition?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1995003}
I live on a very short street with 14 small family houses. The odd-numbered houses from 1 are on one side of the street, and the even-numbered houses from 2 are on the opposite side (e.g., 1 and 2 are opposite each other). 

On one side of the street, all families have surnames that are colors, and on the other side, the surnames indicate professions.

Szabó and Fazekas live opposite to Zöld and Fehér, respectively, who are both neighbors of Fekete.

Kovács is the father-in-law of Lakatos.

Lakatos lives in a higher-numbered house than Barna. The sum of the house numbers of Lakatos and Barna is equal to the sum of the house numbers of Fehér and Fazekas. Kádárné's house number is twice the house number of her sister, Kalaposné.

Sárga lives opposite Pék.

If Bordóné's house number is two-digit and she lives opposite her sister, Kádárné, what is the house number of Mr. Szürke?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
Calculate the volume enclosed by the paraboloid $x^2 + y^2 = z$, the cylinder $y = x^2$, and the planes $z=0$ and $y = 1$. Additionally, consider the revised condition $0 \le z \le 1$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$\frac{88}{105}$}
$已知函数f(x)=|x-2|,g(x)=|2x+3|-|2x-1|.$
$若f(x+a)\geq g(x)，求a的取值范围.$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$[11/2, +\infty )$}
Find the sum of all the positive integers which have at most three not necessarily distinct prime factors where the primes come from the set $\{ 2, 3, 5, 7 \}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1932}
A volunteer organization is recruiting new members. In the fall, they manage to increase their number by 8%. By the spring, however, membership falls by some percentage. The total change in percentage from fall to spring is 12.52%. What was the percentage decrease in the spring?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19.00\%}
It is known that $\operatorname{tg} \alpha$ and $\operatorname{tg} 3 \alpha$ are integers. Find all possible values of $\operatorname{tg} \alpha$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-1, 0, 1}
Let \(ABC\) be a triangle where \(AB = 9\), \(BC = 10\), and \(CA = 17\). Let \(\Omega\) be its circumcircle, and let \(A_1\), \(B_1\), \(C_1\) be the diametrically opposite points from \(A\), \(B\), and \(C\), respectively, on \(\Omega\). Find the area of the convex hexagon with the vertices \(A, B, C, A_1, B_1, C_1\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1155}{4}}
In a tournament with 5 teams, there are no ties. In how many ways can the $\frac{5 \cdot 4}{2}=10$ games of the tournament occur such that no team wins all their games and no team loses all their games?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{544}
Say a real number $r$ is \emph{repetitive} if there exist two distinct complex numbers $z_1, z_2$ with $|z_1| = |z_2| = 1$ and $\{z_1, z_2\} \neq \{-i, i\}$ such that:
\[
z_1(z_1^3 + z_1^2 + rz_1 + 1) = z_2(z_2^3 + z_2^2 + rz_2 + 1).
\]
There exist real numbers $a, b$ such that a real number $r$ is \emph{repetitive} if and only if $a < r \le b$. If the value of $|a| + |b|$ can be expressed in the form $\frac{p}{q}$ for relatively prime positive integers $p$ and $q$, find $100p + q$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2504}
In the geometric sequence {a_n}, a_1 = 9 and a_5 = a_3 * a_4^2. Find the value of a_4. Express your answer as a numerical value, including the ± symbol if necessary.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{± 1/3}
Evaluate the following limit:

$$\lim_{n \to \infty} \sum_{k=n}^{2n-1} \frac{1}{n+\sqrt{k+1}}$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
设 f(x)=\ds{n=0}{\infty}2^{-n}\cos nx，记 A=\int_0^{2\pi}|f(x)|^2\dd x，求 [10A].
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{73}
Rhona wrote down a list of nine multiples of ten: $10, 20, 30, 40, 50, 60, 70, 80, 90$. She then deleted some of these multiples so that the product of the remaining multiples was a square number. What is the least number of multiples that she could have deleted? Express your answer as a whole number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2}
2. On a sheet of lined paper, two rectangles are outlined. The first rectangle has a vertical side shorter than the horizontal side, while the second has the opposite. Find the maximum possible area of their common part, if the first rectangle contains 2015 cells, and the second - 2016.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1302}
10. The base of the right prism $A B C A_{1} B_{1} C_{1}$ is a triangle $A B C$ with angle $B$ equal to $90^{\circ}$ and angle $C$ equal to $30^{\circ}$. Find the area of the section of the prism by a plane passing through the center of the lateral face $A A_{1} C_{1} C$ and vertex $B$ and parallel to the diagonal of the lateral face $A B_{1}$, if the distance from vertex $C$ to the cutting plane is 2, and the hypotenuse of the base of the prism is $\sqrt{14}$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{21}{8}}
Alice has three daughters, each of whom has two daughters. Each of Alice's six grand-daughters has one daughter. How many sets of women from the family of $16$ can be chosen such that no woman and her daughter are both in the set? (Include the empty set as a possible set.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2926}
Find the fourth order partial derivative $K_{xxxy}$ of the function $K(x,y)$ defined as:

$$ K_x = \lim_{h \to 0} \frac{y[(x+h)(x+1)]^{2019} - y[x(x+h+1)]^{2019}}{h(x+1)^{2019}(x+h+1)^{2019}} $$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{0}
1. How many five-digit numbers have the first digit equal to the last, the digit in the thousands place equal to the digit in the tens place, and the product of all digits equal to the square of a natural number?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{243}
The numbers $a, b, c, d$ belong to the interval $[-6.5, 6.5]$. Find the maximum value of the expression $a + 2b + c + 2d - ab - bc - cd - da$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{182}
Find all three-digit integers $\overline{abc} = n$, such that $\frac{2n}{3} = a! \times b! \times c!$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{432}
I have recently come across iterated integrals of the form $$\int_0^tdt_1(t-t_1)^{-1/2}\int_0^{t_1}dt_2 (t_1-t_2)^{-1/2}\cdots\int_{0}^{t_{m-1}}dt_m(t_{m-1}-t_m)^{-1/2}. \tag{1}$$ I am wondering if there is a closed formula for these expressions for general $m$. If $m=2$, then the expression above reduces to $$2\int_0^t dt_1 (t-t_1)^{-1/2} t_1^{1/2} = 2t\int_0^1d\tau(1-\tau)^{-1/2}\tau^{1/2} = \pi t.$$ But it's not clear to me how to generalize this to $m>2$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(\pi t)^{m/2}/\Gamma(1+m/2)}
The radius of a right circular cylinder is decreased by $20\%$ and its height is increased by $25\%$. What is the absolute value of the percent change in the volume of the cylinder?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
Little Johnny invested $10,000. He put part of it in a bank at 5 percent interest and the remainder in bonds which pay a 9 percent annual return. He invested $6,000 in each method (savings bank and bond). What was his annual income from the two investments?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\$660}
If  $ABCDE$  is a regular pentagon and  $X$  is a point in its interior such that  $CDX$  is equilateral, compute  $\angle{AXE}$  in degrees.

*2020 CCA Math Bonanza Lightning Round #1.3*
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{84^\circ}
How many four-digit positive integers have no adjacent equal even digits? For example, count numbers such as $1164$ and $2035$ but not $6447$ or $5866$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{7801}
Peggy has 6 dolls. Her grandmother gives Peggy her own collection of 28 dolls. Over the year, Peggy receives half that amount of dolls for her birthday. She loses 10% of her total dolls during a spring cleaning mishap. For Easter, she receives one-third of the birthday gift amount, and her friend gifts her another doll in exchange for 2 of Peggy's dolls. At Christmas, Peggy gets 20% more dolls than the number of Easter dolls, but her dog chews up and ruins 3 of her dolls. After all these events, how many dolls does Peggy now have?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{50}
A box contains 5 white balls and 3 black balls. What is the probability that when drawing the balls one at a time, all draws alternate in color starting with a white ball?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{56}}
Let a constant $a$ make the equation $\sin x + \sqrt{3}\cos x = a$ have exactly three different solutions $x_{1}$, $x_{2}$, $x_{3}$ in the closed interval $\left[0,2\pi \right]$. The set of real numbers for $a$ is ____.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\{\sqrt{3}\}}
The smallest two-digit number that can be formed by two of 0, 3, 4, 6, and 8 is subtracted by a certain number and it became 7. Find the number.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{23}
Square $PQRS$ has side length $2$ units. Points $T$ and $U$ are on sides $PQ$ and $SQ$, respectively, with $PT = SU$. When the square is folded along the lines $RT$ and $RU$, sides $PR$ and $SR$ coincide and lie on diagonal $RQ$. Find the length of segment $PT$ which can be expressed in the form $\sqrt{k}-m$ units. What is the integer value of $k+m$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{10}
In $\triangle ABC$, the sides $a$, $b$, $c$ are opposite to angles $A$, $B$, $C$, respectively. If $a^{2}+b^{2}=2018c^{2}$, then $\dfrac {2\sin A\sin B\cos C}{1-\cos ^{2}C}=$ \_\_\_\_\_\_.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2017}
Given that the terminal side of angle θ passes through point P(-x, -6) and $$cosθ=- \frac {5}{13}$$, find the value of $$tan(θ+ \frac {π}{4})$$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\frac {17}{7}}
10. In $\triangle A B C$, let $D, E$, and $F$ be points on sides $B C, C A$, and $A B$, respectively, so that the segments $A D, B E$, and $C F$ are concurrent at point $P$. If $A F: F B=4: 5$ and the ratio of the area of $\triangle A P B$ to that of $\triangle A P C$ is $1: 2$, determine $A E: A C$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2:7}
Find the smallest positive integer,  $n$ , which can be expressed as the sum of distinct positive integers  $a,b,c$  such that  $a+b,a+c,b+c$  are perfect squares.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{55}
Let \( S = \{1, 2, 4, 8, 16, 32, 64, 128, 256\} \). A subset \( P \) of \( S \) is called squarely if it is nonempty and the sum of its elements is a perfect square. A squarely set \( Q \) is called super squarely if it is not a proper subset of any squarely set. Find the number of super squarely sets. (A set \( A \) is said to be a proper subset of a set \( B \) if \( A \) is a subset of \( B \) and \( A \neq B \).)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
For Gwen's birthday, she received 8 dollars from her mom. Her dad gave her some more money. If she spent 4 dollars and received 3 more dollars from her mom than she did from her dad, how much money did she receive from her dad?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Given that 60% of all students in Ms. Hanson's class answered "Yes" to the question "Do you love science" at the beginning of the school year, 40% answered "No", 80% answered "Yes" and 20% answered "No" at the end of the school year, calculate the difference between the maximum and the minimum possible values of y%, the percentage of students that gave a different answer at the beginning and end of the school year.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{40\%}
6. Let $\left(x_{1}, x_{2}, \cdots, x_{20}\right)$ be a permutation of $(1,2, \cdots, 20)$, and satisfy
$$
\sum_{i=1}^{20}\left(\left|x_{i}-i\right|+\left|x_{i}+i\right|\right)=620 \text {. }
$$

Then the number of such permutations is. $\qquad$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(10!)^{2}}
Given a small cube block, each face is painted with a different color. If you want to carve 1, 2, 3, 4, 5, 6 small dots on the faces of the block, and the dots 1 and 6, 2 and 5, 3 and 4 are carved on opposite faces respectively, determine the number of different carving methods.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{48}
Let \(\left(x_{1}, x_{2}, \cdots, x_{20}\right)\) be a permutation of \((1, 2, \cdots, 20)\), such that it satisfies
\[ 
\sum_{i=1}^{20}\left(\left|x_{i}-i\right|+\left|x_{i}+i\right|\right) = 620.
\]
How many such permutations exist?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(10!)^2}
George donated 40% of his monthly income to charity. Of the remaining income, he paid 25% in taxes, saved 20% for future use, and spent $50 on groceries and $75 on transportation costs. If he now has $150 left for entertainment and miscellaneous expenses, how much was his monthly income?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$763.89$}
A part of a book has fallen out. The number of the first fallen page is 387, and the number of the last page consists of the same digits but in a different order. How many sheets fell out of the book?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{176}