inclusionAI/Ring-lite-rl-data huggingface dataset:
Given three equilateral triangles $\triangle HOW$, $\triangle BOW$, and $\triangle DAH$ in a plane:
- $WO = 7$
- $AH = 2$

It is also given that the points $D$, $A$, and $B$ are collinear in that order. 

Find the length of $BA$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{11}
How many ways are there to arrange the letters of the word $\text{B}_1\text{A}_1\text{N}_1\text{A}_2\text{N}_2\text{A}_3\text{B}_2$, where three A's, two N's, and two B's are all considered different within each letter group but identical between groups?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{210}
On a seven-day trip, Carrie drove 135 miles the first day, 124 miles more the second day, 159 miles the third day, 189 miles the fourth day, 210 miles the fifth day, 156 miles the sixth day, and 240 miles the seventh day. If her phone had a charging capacity that lasted for 106 miles initially, but increased by an increment of 15 miles every day, how many times did she charge her phone for the whole trip?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{14}
Let us consider all rectangles with sides of length $a$ and $b$, both of which are whole numbers. Do more of these rectangles have a perimeter of $2000$ or a perimeter of $2002$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2002}
A five-digit number is called irreducible if it cannot be expressed as a product of two three-digit numbers.

What is the greatest number of consecutive irreducible five-digit numbers?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{99}
The generatrix of a cone forms an angle $\alpha$ with the plane of its base, $\cos \alpha=\frac{1}{4}$. A sphere is inscribed in the cone, and a plane is drawn through the circle of contact between the sphere and the lateral surface of the cone. The volume of the part of the cone enclosed between this plane and the base plane of the cone is 37. Find the volume of the remaining part of the cone.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{27}
The Red Sox play the Yankees in a best-of-seven series that ends as soon as one team wins four games. Suppose that the probability that the Red Sox win Game \( n \) is \(\frac{n-1}{6}\). What is the probability that the Red Sox will win the series?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{2}}
Points $D$ and $E$ are marked on the sides $AC$ and $BC$ of triangle $ABC$ respectively, such that $AD = EC$. It turns out that $BD = ED$ and $\angle BDC = \angle DEB$. Find the length of the segment $AC$, given that $AB = 7$ and $BE = 2$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12}
For how many positive integers $n \le 500$ is $n!$ divisible by $2^{n-2}$?

[i]Proposed by Eugene Chen[/i]
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{44}
设 $f(x)=\frac{1}{x^{3}-x}$, 求满足不等式 $f(2)+f(3)+\cdots+f(n)>\frac{499}{2020}$ 的最小正整数 $n$. 请给出$n$的值。
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{13}
We select a real number $\alpha$ uniformly and at random from the interval $(0,500)$. Define 
\[ S = \frac{1}{\alpha} \sum_{m=1}^{1000} \sum_{n=m}^{1000} \left\lfloor \frac{m+\alpha}{n} \right\rfloor. \]
Let $p$ denote the probability that $S \ge 1200$. Compute $1000p$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
Consider an infinite grid of equilateral triangles. Each edge (that is, each side of a small triangle) is colored one of \( N \) colors. The coloring is done in such a way that any path between any two nonadjacent vertices consists of edges with at least two different colors. What is the smallest possible value of \( N \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Given that $x=x_{1}$ and $x=x_{2}$ are respectively the local minimum and maximum points of the function $f\left(x\right)=2a^{x}-ex^{2}$ where $a \gt 0$ and $a\neq 1$. If $x_{1} \lt x_{2}$, then the range of values for $a$ is $\underline{\hspace{1cm}}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\left(\frac{1}{e}, 1\right)}
A 480 m long train is running at a speed of 55 km/hr. It crossed a platform of a certain length in 71.99424046076314 seconds. What is the length of the platform?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{620}
Rationalize the denominator of $\frac{5}{4\sqrt{7} + 3\sqrt{13}}$ and express your answer in the form $\frac{A\sqrt{B} + C\sqrt{D}}{E}$ where $B < D$, the fraction is in lowest terms, and all radicals are in simplest radical form. What is $A+B+C+D+E$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
设整数 n>4，(x+2\sqrt{y}-1)^n 的展开式中 x^{n-4} 与 xy 两项的系数相等，则 n 的值为________.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{51}
What is the smallest possible area of a right-angled triangle whose hypotenuse contains the point \( M(1, 3) \) and whose legs lie on the lines \( y = x \) and \( y = -x \)?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
A school organizes a trip for teachers and students. If they rent several 48-seat buses, they can fill them exactly. If they rent 64-seat buses, they can rent one less bus, and there will be one bus that is not fully occupied but is more than half full. Knowing that renting a 48-seat bus costs 260 yuan per bus and renting a 64-seat bus costs 300 yuan per bus, which type of bus is more cost-effective to rent?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{64\text{-seat buses}}
A positive integer $n$ is called *nice* if it has at least 3 proper divisors and it is equal to the sum of its three largest proper divisors. For example, $6$ is *nice* because its largest three proper divisors are $3, 2, 1$ and $6 = 3 + 2 + 1$. Find the number of *nice* integers not greater than $3000$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{200}
11. In the Kingdom of Fantasy, the way of representing numbers is quite unique. If a number or a part of a number consists of consecutive digits, it must be written in another form. For example, what we write as 12345, they must write as $1 ※ 5$; what we write as 134569, they must write as $13 ※ 69$; what we write as 7543210, they must write as $75 ※ 0$. Of course, there are also troublesome times, such as 98, which they must write as $9 ※ 8$. The following calculation problem is a math question from the Kingdom of Fantasy. Please calculate the correct result (expressed in the normal way).
$$
20 ※ 13 + 20 ※ 3 + 2 ※ 0 ※ 13 =
$$
$\qquad$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{43149}
Given a positive integer $n$ with prime factorization $p_1^{e_1}p_2^{e_2}... p_k^{e_k}$ , we define $f(n)$ to be  $\sum^k_{i=1}p_ie_i$. In other words, $f(n)$ is the sum of the prime divisors of $n$, counted with multiplicities. Let $M$ be the largest odd integer such that $f(M) = 2023$, and $m$ the smallest odd integer so that $f(m) = 2023$. Suppose that $\frac{M}{m}$ equals $p_1^{e_1}p_2^{e_2}... p_l^{e_l}$ , where the $e_i$ are all nonzero integers and the $p_i$ are primes. Find $\left| \sum^l_{i=1} (p_i + e_i) \right|$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2695}
在平面直角坐标系 $x O y$, 点集 $K=\{(x, y) \mid x, y \in-1,0,1\}$ 。在 $K$ 中随机取出三个点,则这三个点两两之间的距离均不超过 2 的概率是 $\qquad$.原始的答案是\frac{m}{n}的形式，其中m、n是互质的。请给出最终m + n的值
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{19}
When $p = \sum\limits_{k=1}^{6} k \ln{k}$, the number $e^p$ is an integer.  What is the largest power of 2 that is a factor of $e^p$ ?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2^{16}}
8,9

The acute angle of an isosceles trapezoid is $75^{\circ}$. Lines passing through the ends of one of the bases of the trapezoid, parallel to the opposite lateral sides, intersect on the circle circumscribed around the trapezoid. Find the ratio of the bases of the trapezoid.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{3}}
Select several numbers from $1, 2, 3, \cdots, 9, 10$ so that every number among $1, 2, 3, \cdots, 19, 20$ can be expressed as either one of the selected numbers or the sum of two selected numbers (which can be the same). What is the minimum number of selections needed?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
On the edge of a dihedral angle of $120^{\circ}$, a segment of length $c$ is taken, and from its ends, perpendiculars to it are drawn, lying in different faces of the given dihedral angle and having lengths $a$ and $b$. Find the length of the segment of the line connecting the ends of these perpendiculars.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\sqrt{a^2 + b^2 + a b + c^2}}
Given a function $f(x)$ with domain $\mathbb{R}$ and its derivative $f'(x)$, it satisfies $f'(x) - 2f(x) > 4$. If $f(0) = -1$, then the solution set of the inequality $f(x) + 2 > e^{2x}$ is ______.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{(0, +\infty)}
Let $b_n$ be the number obtained by writing the integers 1 to $n$ from left to right in reverse order. For example, $b_4 = 4321$ and $b_{12} = 121110987654321$. For $1 \le k \le 150$, how many $b_k$ are divisible by 9?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{32}
Evaluate the expression $\dfrac{\sqrt[6]{5}}{\sqrt[4]{5}}$. What power of 5 does this expression represent?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{-\frac{1}{12}}
Three swimmers have to swim a 50-meter lane in the pool, immediately turn back and return to the starting point. The first swimmer starts first, the second swimmer starts 5 seconds later, and the third swimmer starts another 5 seconds after the second. At some point in time, before reaching the end of the lane, all three swimmers were equidistant from the start. The third swimmer, having reached the end of the lane and turning back, met the second swimmer 4 meters from the end of the lane, and the first swimmer 7 meters from the end of the lane. Find the speed of the third swimmer.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{22}{15} \, \text{m/s}}
A certain clock rings 2 notes at quarter past the hour, 4 notes at half past, and 6 notes at 3-quarters past. On the hour, it rings some notes plus an additional number of notes equal to whatever hour it is. The clock will ring 103 notes from 1:00 p.m. through 5:00 p.m., including the rings at 1:00 and 5:00. How many base notes does the clock ring on the hour, before adding the additional notes equal to the hour?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{8}
Find the maximum value of the expression $\left|e^{i\theta}-a\right|+\left|e^{i\theta}+a\right|$ for $0\le\theta\le2\pi$ and $a\in\mathbb{R}$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2\sqrt{a^2+1}}
Given a convex quadrilateral with area \( S \). A point inside it is chosen and reflected symmetrically with respect to the midpoints of its sides. This results in four vertices of a new quadrilateral. Find the area of the new quadrilateral.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{2S}
The perimeter of a square is equal to the radius of a circle. The area of the square is 784.3155595568603 sq cm. What is the area of the circle?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{39424}
Angle $2023^{\circ}$ lies in the ______ quadrant.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{third}
已知 $x, y, z$ 均为正整数, 且 $\frac{x(y+1)}{x-1}, \frac{y(z+1)}{y-1}, \frac{z(x+1)}{z-1}$ 均为正整数, 则 $x y z$ 的最大值和最小值之和为 $\qquad$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{701}
The domain of the function $y=\sin x$ is $[a,b]$, and its range is $\left[-1, \frac{1}{2}\right]$. Find the maximum value of $b-a$. Express your answer as a single value in radians, simplified if possible.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{4\pi}{3}}
Given 2005 distinct numbers  $a_1,\,a_2,\dots,a_{2005}$ . By one question, we may take three different indices  $1\le i<j<k\le 2005$  and find out the set of numbers  $\{a_i,\,a_j,\,a_k\}$  (unordered, of course).  Find the minimal number of questions, which are necessary to find out all numbers  $a_i$ .
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1003}
Given the function
$$
f(x)=\left(1-x^{2}\right)\left(x^{2}+b x+c\right) \text{ for } x \in [-1, 1].
$$

Let $\mid f(x) \mid$ have a maximum value of $M(b, c)$. As $b$ and $c$ vary, find the minimum value of $M(b, c)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3 - 2\sqrt{2}}
Eleven girls and \( n \) boys went to the forest to pick mushrooms. Together, they collected \( n^{2} + 9n - 2 \) mushrooms, and each of them collected an equal number of mushrooms.

Who were more in number: boys or girls?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Girls}
In triangle $ABC,$ $D,$ $E,$ and $F$ are points on sides $\overline{BC},$ $\overline{AC},$ and $\overline{AB},$ respectively, so that $BD:DC = CE:EA = AF:FB = 1:2.$

[asy]
unitsize(0.8 cm);

pair A, B, C, D, E, F, P, Q, R;

A = (2,5);
B = (0,0);
C = (7,0);
D = interp(B,C,1/3);
E = interp(C,A,1/3);
F = interp(A,B,1/3);
P = extension(A,D,C,F);
Q = extension(A,D,B,E);
R = extension(B,E,C,F);

fill(P--Q--R--cycle,gray(0.7));
draw(A--B--C--cycle);
draw(A--D);
draw(B--E);
draw(C--F);

label("$A$", A, N);
label("$B$", B, SW);
label("$C$", C, SE);
label("$D$", D, S);
label("$E$", E, NE);
label("$F$", F, W);
label("$P$", P, NE);
label("$Q$", Q, NW);
label("$R$", R, S);
[/asy]

Line segments $\overline{AD},$ $\overline{BE},$ and $\overline{CF}$ intersect at $P,$ $Q,$ and $R,$ as shown above.  Compute $\frac{[PQR]}{[ABC]}.$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{1}{7}}
The instantaneous rate of change of carbon-14 content is $-\frac{\ln2}{20}$ (becquerel/year) given that at $t=5730$. Using the formula $M(t) = M_0 \cdot 2^{-\frac{t}{5730}}$, determine $M(2865)$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{573\sqrt{2}/2}
In the polar coordinate system, $P$ is a moving point on the curve $\rho=12\sin \theta$, and $Q$ is a moving point on the curve $\rho=12\cos (\theta- \frac {\pi}{6})$. Find the maximum value of $PQ$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{18}
A carpenter worked alone for 1 day on a job. He and another carpenter completed the job in 2 more days. It would have taken the second carpenter 5 days to do the complete job working alone. How many more days would it have taken the first carpenter to finish the job alone?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
Let $n$ be a positive integer. All numbers $m$ which are coprime to $n$ satisfy $m^6 \equiv 1 \pmod{n}$. Find the maximum possible value of $n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{504}
On the first day, $2^n$ students played a knockout table tennis tournament: first, two played, then the winner played against the third, the winner of that pair played against the fourth, and so on, until the last student played (draws are not possible in table tennis).

On the second day, the same students competed for a cup: they randomly paired up and played in pairs, the losers were eliminated, and the winners were randomly paired up again and played in pairs, and so on. It turned out that the sets of pairs that played on the first and second days were the same (possibly with different winners). Find the largest possible value of $n$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{3}
In an acute scalene triangle  $ABC$ , points  $D,E,F$  lie on sides  $BC, CA, AB$ , respectively, such that  $AD \perp BC, BE \perp CA, CF \perp AB$ . Altitudes  $AD, BE, CF$  meet at orthocenter  $H$ . Points  $P$  and  $Q$  lie on segment  $EF$  such that  $AP \perp EF$  and  $HQ \perp EF$ . Lines  $DP$  and  $QH$  intersect at point  $R$ . Compute  $HQ/HR$ .

*Proposed by Zuming Feng*
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{1}
The telephone company wants to add an area code composed of 2 letters to every phone number. In order to do so, the company chose a special sign language containing 124 different signs. The company used some of the signs fully and two remained unused. The company can create 488 additional area codes if they use all 124 signs. How many signs were used fully by the company?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{120}
When two perpendicular lines are rotated about each other (out of their common plane), what is the new angle between them?

More formally: Let $\ell$ and $m$ be two perpendicular lines, and let their common plane be $P$. Rotate $\ell$ about $m$ out of plane $P$ by angle $\theta$, and rotate $m$ about $\ell$ out of plane $P$ by angle $\phi$. Now $\ell'$ and $m'$ have common plane $Q$. What is the angle $\psi$ between $\ell'$ and $m'$?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\arccos(\sin\theta \sin\phi)}
Suppose hops, skips and jumps are specific units of length. If $b$ hops equals $c$ skips, $d$ jumps equals $e$ hops, and $f$ jumps equals $g$ meters, then one meter equals how many skips?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{$\frac{cef}{bdg}$}
Two players play on an $8 \times 8$ chessboard. The player who starts the game makes the first move - placing a knight on the board. Then they take turns moving it (according to the usual rules), and it is not allowed to place the knight on a square where it has already been. The player who has no legal moves loses. Who wins with correct play - the starting player or their partner?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Partner}
When \( x \in [1, 2017] \), find the minimum value of
$$
f(x) = \sum_{i=1}^{2017} i |x - i|
$$
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{801730806}
A projectile is fired with an initial speed $v$ from the ground at an angle between $0^\circ$ and $90^\circ$ to the horizontal. The trajectory of the projectile can be described by the parametric equations
\[
x = vt \cos \theta, \quad y = vt \sin \theta - \frac{1}{2} gt^2,
\]
where $t$ is the time, $g$ is the acceleration due to gravity, and $\theta$ varies from $0^\circ$ to $90^\circ$. As $\theta$ varies within this range, the highest points of the projectile paths trace out a curve. Calculate the area enclosed by this curve, which can be expressed as $c \cdot \frac{v^4}{g^2}$. Find the value of $c$.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\pi}{16}}
The cash realized on selling a 14% stock is Rs. 108.25, with the brokerage being 1/4%. What is the net amount received after deducting the brokerage?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{107.98}
There are 20 rooms, with some lights on and some lights off. The people in these rooms want to have their lights in the same state as the majority of the other rooms. Starting with the first room, if the majority of the remaining 19 rooms have their lights on, the person will turn their light on; otherwise, they will turn their light off. Initially, there are 10 rooms with lights on and 10 rooms with lights off, and the light in the first room is on. After everyone has had their turn, how many rooms will have their lights off?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{20}
Eight friends, Aerith, Bob, Chebyshev, Descartes, Euler, Fermat, Gauss, and Hilbert, bought tickets for adjacent seats at the opera. However, when they arrived, they mixed up their seats:

- Bob sat in his assigned seat.
- Chebyshev sat two seats to the right of Gauss' assigned seat.
- Descartes sat one seat to the left of Fermat's assigned seat.
- Euler sat four seats to the left of Hilbert's assigned seat.
- Fermat sat five seats to the right of Descartes' assigned seat.
- Gauss sat one seat to the right of Euler's assigned seat.
- Hilbert sat three seats to the left of Aerith's assigned seat.

In whose seat did Aerith sit?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Chebyshev}
Given that points P1 and P2 are two adjacent centers of symmetry for the curve $y= \sqrt {2}\sin ωx-\cos ωx$ $(x\in\mathbb{R})$, if the tangents to the curve at points P1 and P2 are perpendicular to each other, determine the value of ω.
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{\frac{\sqrt{3}}{3}}
Find the maximum value that the expression \(a e k - a f h + b f g - b d k + c d h - c e g\) can take, given that each of the numbers \(a, b, c, d, e, f, g, h, k\) equals \(\pm 1\).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4}
给定 1991 个集合, 其中每个集合中都恰好有 45 个元素, 并且每两个集合的并集中都恰好有 89 个元素. 试问, 这 1991 个集合的并集中含有多少个元素?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{87605}
A license plate in a certain state consists of 5 digits, not necessarily distinct, and 3 letters, with the condition that at least one of the letters must be a vowel (A, E, I, O, U). These letters do not need to be next to each other but must be in a sequence. How many distinct license plates are possible if the digits and the letter block can appear in any order?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{4,989,000,000}
Last year, 10% of the net income from our school's ball was allocated to clubs for purchases, and the remaining part covered the rental cost of the sports field. This year, we cannot sell more tickets, and the rental cost remains the same, so increasing the share for the clubs can only be achieved by raising the ticket price. By what percentage should the ticket price be increased to make the clubs' share 20%?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{12.5}
We call a number greater than  $25$ , *semi-prime* if it is the sum of some two different prime numbers. What is the greatest number of consecutive natural numbers that can be *semi-prime*?
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{5}
When $11^4$ is written out in base 10, the sum of its digits is $16=2^4$. What is the largest base $b$ such that the base-$b$ digits of $11^4$ do not add up to $2^4$?  (Note: here, $11^4$ in base $b$ means that the base-$b$ number $11$ is raised to the fourth power.)
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{6}
Given that July 1, 1997, was a Tuesday, determine the day of the week for June 9, 1898. Express your answer as the full day of the week (e.g., Monday, Tuesday, etc.).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{Thursday}
Let \( a \) and \( b \) be positive integers such that \( 79 \mid (a + 77b) \) and \( 77 \mid (a + 79b) \). Find the smallest possible value of \( a + b \).
Please reason step by step, and put your final answer within \boxed{}.
Answer: \boxed{193}