alexjercan/bugnet huggingface dataset:
Iron Bars

A boy PCK had N straight iron bars, which were serially indexed. Unfortunately, the first M bars (0 ≤ M ≤ N) among them were bent during transportation. They all suffered a perpendicular bend at one point.

He is planning to make a cube using a set of bars selected using the following rules: X bars from bent ones, Y bars from straight ones, where 2X + Y = 12. Any two bars can be jointed only at the apexes of the cube. He wants to count how many types of rectangular parallelepipeds (hereafter RP) he can make using these bars.

Make a program to count out types (different shapes) of RPs that PCK can make using the following information: the number of bars and length of each one, position of the bend, and the number of bars to be used to construct an RP. Note that any two RPs similar in shape are considered identical: namely if the length of three defining sides of two RPs coincide if arranged in increasing/decreasing order (e.g., three sides of RP i and j are A_i, B_i, C_i, and A_j, B_j and C_j in increasing order, then the relations A_i = A_j, B_i = B_j, and C_i = C_j hold. Note also that the bars are sufficiently thin to allow you to consider them as idealized lines.

Input

The input is given in the following format.

N M X Y
a_1
a_2
:
a_N
b_1
b_2
:
b_M

The first line provides the total number of iron bars and bent bars, and those straight and bent bars used to construct an RP: N (6 ≤ N ≤ 6000), M (0 ≤ M ≤ N), X (0 ≤ X ≤ 6), and Y (0 ≤ Y ≤ 12). The following relations always hold for them: 2X+Y=12, X+Y ≤ N, X ≤ M. Each of the subsequent N lines provides the length of the i-th bar a_i (1 ≤ a_i ≤ 6000) in integers. Furthermore, each of the subsequent M lines provides the location at which the i-th bent bar suffered a perpendicular bend b_i (1 ≤ b_i ≤ 3000) in centimeters from one end of the bar (note: 1 ≤ a_i-b_i ≤ 3000).

Output

Output the number of constructible rectangular parallelepipeds.

Sample Input 1

18 8 3 6
4
3
3
3
3
2
2
2
1
1
1
1
1
2
2
3
3
3
1
1
1
1
1
1
1
1

Sample Output 1

3
Celsius/Fahrenheit

In Japan, temperature is usually expressed using the Celsius (℃) scale. In America, they used the Fahrenheit (℉) scale instead. $20$ degrees Celsius is roughly equal to $68$ degrees Fahrenheit. A phrase such as "Today’s temperature is $68$ degrees" is commonly encountered while you are in America.

A value in Fahrenheit can be converted to Celsius by first subtracting $32$ and then multiplying by $\frac{5}{9}$. A simplified method may be used to produce a rough estimate: first subtract $30$ and then divide by $2$. Using the latter method, $68$ Fahrenheit is converted to $19$ Centigrade, i.e., $\frac{(68-30)}{2}$.

Make a program to convert Fahrenheit to Celsius using the simplified method: $C = \frac{F - 30}{2}$.

Input

The input is given in the following format.

$F$

The input line provides a temperature in Fahrenheit $F$ ($30 \leq F \leq 100$), which is an integer divisible by $2$.

Output

Output the converted Celsius temperature in a line.

Sample Input 1

68

Sample Output 1

19

Sample Input 2

50

Sample Output 2

10
Red Dragonfly

It’s still hot every day, but September has already come. It’s autumn according to the calendar. Looking around, I see two red dragonflies at rest on the wall in front of me. It’s autumn indeed.

When two red dragonflies’ positional information as measured from the end of the wall is given, make a program to calculate the distance between their heads.

Input

The input is given in the following format.

$x_1$ $x_2$

The input line provides dragonflies’ head positions $x_1$ and $x_2$ ($0 \leq x_1, x_2 \leq 100$) as integers.

Output

Output the distance between the two red dragonflies in a line.

Sample Input 1

20 30

Sample Output 1

10

Sample Input 2

50 25

Sample Output 2

25

Sample Input 3

25 25

Sample output 3

0
Cake Party

I’m planning to have a party on my birthday. Many of my friends will come to the party. Some of them will come with one or more pieces of cakes, but it is not certain if the number of the cakes is a multiple of the number of people coming.

I wish to enjoy the cakes equally among the partiers. So, I decided to apply the following rules. First, all the party attendants are given the same number of cakes. If some remainder occurs, a piece goes on a priority basis to the party host (that’s me!). How many pieces of cake can I enjoy?

Given the number of my friends and cake information, make a program to calculate how many pieces of cake I can enjoy. Note that I am not counted in the number of my friends.

Input

The input is given in the following format.

$N$ $C$
$p_1$ $p_2$ ... $p_C$

The first line provides the number of my friends $N$ ($1 \leq N \leq 100$) and the number of those among them who brought one or more pieces of cake with them $C$ ($1 \leq C \leq N$). The second line provides an array of integers $p_i$ ($1 \leq p_i \leq100$), each of which shows the number of cakes of the $i$-th friend of mine who was willing to come up with one or more pieces of cake.

Output

Output the number of cakes I can enjoy.

Sample Input 1

5 4
5 5 6 5

Sample Output 1

4

Sample Input 2

7 5
8 8 8 8 8

Sample Output 2

5

Sample Input 3

100 3
3 3 3

Sample Output 3

1
Heat Stroke

We have had record hot temperatures this summer. To avoid heat stroke, you decided to buy a quantity of drinking water at the nearby supermarket. Two types of bottled water, 1 and 0.5 liter, are on sale at respective prices there. You have a definite quantity in your mind, but are willing to buy a quantity larger than that if: no combination of these bottles meets the quantity, or, the total price becomes lower.

Given the prices for each bottle of water and the total quantity needed, make a program to seek the lowest price to buy greater than or equal to the quantity required.

Input

The input is given in the following format.

$A$ $B$ $X$

The first line provides the prices for a 1-liter bottle $A$ ($1\leq A \leq 1000$), 500-milliliter bottle $B$ ($1 \leq B \leq 1000$), and the total water quantity needed $X$ ($1 \leq X \leq 20000$). All these values are given as integers, and the quantity of water in milliliters.

Output

Output the total price.

Sample Input 1

180 100 2400

Sample Output 1

460

Sample Input 2

200 90 2018

Sample Output 2

450
Dudeney Number

A Dudeney number is a positive integer for which the sum of its decimal digits is equal to the cube root of the number. For example, $512$ is a Dudeney number because it is the cube of $8$, which is the sum of its decimal digits ($5 + 1 + 2$).

In this problem, we think of a type similar to Dudeney numbers and try to enumerate them.

Given a non-negative integer $a$, an integer $n$ greater than or equal to 2 and an upper limit $m$, make a program to enumerate all $x$’s such that the sum of its decimal digits $y$ satisfies the relation $x = (y + a)^n$, and $x \leq m$.

Input

The input is given in the following format.

$a$ $n$ $m$

The input line provides three integers: $a$ ($0 \leq a \leq 50$), $n$ ($2 \leq n \leq 10$) and the upper limit $m$ ($1000 \leq m \leq 10^8$).

Output

Output the number of integers that meet the above criteria.

Sample Input 1

16 2 1000

Sample Output 1

2

Two: $400 = (4 + 0 + 0 + 16)^2$ and $841 = (8 + 4 + 1 + 16)^2$

Sample Input 2

0 3 5000

Sample Output 2

3

Three: $1=1^3$, $512 = (5 + 1 + 2)^3$ and $4913 = (4 + 9 + 1 + 3)^3$.

Sample Input 3

2 3 100000

Sample Output 3

0

There is no such number $x$ in the range below $100,000$ such that its sum of decimal digits $y$ satisfies the relation $(y+2)^3 = x$.
Bozosort

Bozosort, as well as Bogosort, is a very inefficient sort algorithm. It is a random number-based algorithm that sorts sequence elements following the steps as below:

Randomly select two elements and swap them.

Verify if all the elements are sorted in increasing order.

Finish if sorted, else return to 1.

To analyze Bozosort, you have decided to simulate the process using several predetermined pairs of elements.

You are given several commands to swap two elements. Make a program to evaluate how many times you have to run the command before the sequence is aligned in increasing order.

Input

The input is given in the following format.

$N$
$a_1$ $a_2$ ... $a_N$
$Q$
$x_1$ $y_1$
$x_2$ $y_2$
$...$
$x_Q$ $y_Q$

The first line provides the number of sequence elements $N$ ($2 \leq N \leq 300,000$). The second line provides an array of integers $a_i$ ($1 \leq a_i \leq 10^9$) that constitutes the sequence. Each of the subsequent $Q$ lines provides a pair of integers $x_i,y_i$ ($1 \leq x_i,y_i \leq N$) that represent the $i$-th command, which swaps the two elements indicated by $x_i$ and $y_i$ ($x_i \ne y_i$).

Output

If neat alignment in increasing order is realized the first time after execution of multiple commands, output at what time it was. Output 0 if the initial sequence is aligned in increasing order, and -1 if exhaustive execution still failed to attain the goal.

Sample Input 1

6
9 7 5 6 3 1
3
1 6
2 5
3 4

Sample Output 1

2

Sample Input 2

4
4 3 2 1
2
1 2
3 4

Sample Output 2

-1

Sample Input 3

5
1 1 1 2 2
1
1 2

Sample Input 3

0
Transporter

In the year 30XX, an expedition team reached a planet and found a warp machine suggesting the existence of a mysterious supercivilization. When you go through one of its entrance gates, you can instantaneously move to the exit irrespective of how far away it is. You can move even to the end of the universe at will with this technology!

The scientist team started examining the machine and successfully identified all the planets on which the entrances to the machine were located. Each of these N planets (identified by an index from $1$ to $N$) has an entrance to, and an exit from the warp machine. Each of the entrances and exits has a letter inscribed on it.

The mechanism of spatial mobility through the warp machine is as follows:

If you go into an entrance gate labeled with c, then you can exit from any gate with label c.

If you go into an entrance located on the $i$-th planet, then you can exit from any gate located on the $j$-th planet where $i < j$.

Once you have reached an exit of the warp machine on a planet, you can continue your journey by entering into the warp machine on the same planet. In this way, you can reach a faraway planet. Our human race has decided to dispatch an expedition to the star $N$, starting from Star $1$ and using the warp machine until it reaches Star $N$. To evaluate the possibility of successfully reaching the destination. it is highly desirable for us to know how many different routes are available for the expedition team to track.

Given information regarding the stars, make a program to enumerate the passages from Star $1$ to Star $N$.

Input

The input is given in the following format.

$N$
$s$
$t$

The first line provides the number of the stars on which the warp machine is located $N$ ($2 \leq N \leq 100,000$). The second line provides a string $s$ of length $N$, each component of which represents the letter inscribed on the entrance of the machine on the star. By the same token, the third line provides a string $t$ of length $N$ consisting of the letters inscribed on the exit of the machine. Two strings $s$ and $t$ consist all of lower-case alphabetical letters, and the $i$-th letter of these strings corresponds respectively to the entrance and exit of Star $i$ machine.

Output

Divide the number of possible routes from Star $1$ to Star $N$ obtained above by 1,000,000,007, and output the remainder.

Sample Input 1

6
abbaba
baabab

Sample Output 1

5

Sample Input 2

25
neihsokcpuziafoytisrevinu
universityofaizupckoshien

Sample Output 2

4
Taxi

PCK Taxi in Aizu city, owned by PCK company, has adopted a unique billing system: the user can decide the taxi fare. Today as usual, many people are waiting in a queue at the taxi stand in front of the station.

In front of the station, there are $N$ parking spaces in row for PCK taxis, each with an index running from $1$ to $N$. Each of the parking areas is occupied by a taxi, and a queue of potential passengers is waiting for the ride. Each one in the queue has his/her own plan for how much to pay for the ride.

To increase the company’s gain, the taxi driver is given the right to select the passenger who offers the highest taxi fare, rejecting others.

The driver in the $i$-th parking space can perform the following actions any number of times in any sequence before he finally selects a passenger and starts driving.

Offer a ride to the passenger who is at the head of the $i$-th parking space’s queue.

Reject to offer a ride to the passenger who is at the head of the $i$-th parking space’s queue. The passenger is removed from the queue.

Move to the $i + 1$-th parking area if it is empty. If he is in the $N$-th parking area, he leaves the taxi stand to cruise the open road.

A preliminary listening is made as to the fare the users offer. Your task is to maximize the sales volume of PCK Taxi in reference to the table of offered fares. A taxi cannot accommodate more than one passenger.

Given the number of taxi parking spaces and information regarding the persons waiting in the parking areas, calculate the maximum possible volume of sales.

Input

The input is given in the following format.

$N$
$s_1$
$s_2$
$...$
$s_N$

The first line provides the number of taxi parking areas $N$ ($1 \leq N \leq 300,000$). Each of the subsequent $N$ lines provides information on the customers queueing in the $i$-th taxi parking area in the following format:

$M$ $c_1$ $c_2$ ... $c_M$

The first integer $M$ ($1 \leq M \leq 300,000$) indicates the number of customers in the queue, and the subsequent array of integers $c_j$ ($1 \leq c_j \leq 10,000$) indicates the fare the $j$-th customer in the queue is willing to pay. The total number of customers in the taxi stand is equal to or less than $300,000$.

Output

Output the maximum volume of sales.

Sample Input

3
3 8 10 1
4 7 1 2 15
3 11 8 19

Sample Output

45
Points on a Straight Line

The university of A stages a programming contest this year as has been the case in the past. As a member of the team in charge of devising the problems, you have worked out a set of input data for a problem, which is an arrangement of points on a 2D plane in the coordinate system. The problem requires that any combination of these points greater than or equal to $K$ in number must not align on a line. You want to confirm that your data satisfies this requirement.

Given the number of points $K$ and their respective 2D coordinates, make a program to check if any combination of points greater or equal to $K$ align on a line.

Input

The input is given in the following format.

$N$ $K$
$x_1$ $y_1$
$x_2$ $y_2$
$...$
$x_N$ $y_N$

The first line provides the number of points $N$ ($3 \leq N \leq 3000$) on the 2D coordinate system and an integer $K$ ($3 \leq K \leq N$). Each of the subsequent lines provides the $i$-th coordinate $x_i,y_i$ ($0 \leq x_i,y_i \leq 10000$) as integers. None of these coordinates coincide, i.e., if $i \ne j$, then $x_i \ne x_j$ or $y_i \ne y_j$.

Output

Output 1 if any combination of points greater or equal to $K$ aligns on a line, or 0 otherwise.

Sample Input 1

5 4
0 0
1 0
1 1
0 1
2 2

Sample Output 1

0

Sample Input 2

7 5
0 0
1 0
1 1
0 1
2 0
3 0
4 0

Sample Output 2

1
Dungeon 2

Bob is playing a game called "Dungeon 2" which is the sequel to the popular "Dungeon" released last year. The game is played on a map consisting of $N$ rooms and $N-1$ roads connecting them. The roads allow bidirectional traffic and the player can start his tour from any room and reach any other room by way of multiple of roads. A point is printed in each of the rooms.

Bob tries to accumulate the highest score by visiting the rooms by cleverly routing his character "Tora-Tora." He can add the point printed in a room to his score only when he reaches the room for the first time. He can also add the points on the starting and ending rooms of Tora-Tora’s journey. The score is reduced by one each time Tora-Tore passes a road. Tora-Tora can start from any room and end his journey in any room.

Given the map information, make a program to work out the maximum possible score Bob can gain.

Input

The input is given in the following format.

$N$
$p_1$
$p_2$
$...$
$p_N$
$s_1$ $t_1$
$s_2$ $t_2$
$...$
$s_{N-1}$ $t_{N-1}$

The first line provides the number of rooms $N$ ($1 \leq N \leq 100,000$). Each of the subsequent $N$ lines provides the point of the $i$-th room $p_i$ ($-100 \leq p_i \leq 100$) in integers. Each of the subsequent lines following these provides the information on the road directly connecting two rooms, where $s_i$ and $t_i$ ($1 \leq s_i < t_i \leq N$) represent the numbers of the two rooms connected by it. Not a single pair of rooms are connected by more than one road.

Output

Output the maximum possible score Bob can gain.

Sample Input 1

7
6
1
-1
4
3
3
1
1 2
2 3
3 4
3 5
5 6
5 7

Sample Output 1

10

For example, the score is maximized by routing the rooms in the following sequence: $6 \rightarrow 5 \rightarrow 3 \rightarrow 4 \rightarrow 3 \rightarrow 2 \rightarrow 1$.

Sample Input 2

4
5
0
1
1
1 2
2 3
2 4

Sample Output 2

5

The score is maximized if Tora-Tora stats his journey from room 1 and ends in the same room.
Meeting in a City

You are a teacher at Iazu High School is the Zuia Kingdom. There are $N$ cities and $N-1$ roads connecting them that allow you to move from one city to another by way of more than one road. Each of the roads allows bidirectional traffic and has a known length.

As a part of class activities, you are planning the following action assignment for your students. First, you come up with several themes commonly applicable to three different cities. Second, you assign each of the themes to a group of three students. Then, each student of a group is assigned to one of the three cities and conducts a survey on it. Finally, all students of the group get together in one of the $N$ cities and compile their results.

After a theme group has completed its survey, the three members move from the city on which they studied to the city for getting together. The longest distance they have to travel for getting together is defined as the cost of the theme. You want to select the meeting city so that the cost for each theme becomes minimum.

Given the number of cities, road information and $Q$ sets of three cities for each theme, make a program to work out the minimum cost for each theme.

Input

The input is given in the following format.

$N$ $Q$
$u_1$ $v_1$ $w_1$
$u_2$ $v_2$ $w_2$
$...$
$u_{N-1}$ $v_{N-1}$ $w_{N-1}$
$a_1$ $b_1$ $c_1$
$a_2$ $b_2$ $c_2$
$...$
$a_Q$ $b_Q$ $c_Q$

The first line provides the number of cities in the Zuia Kingdom $N$ ($3 \leq N \leq 100,000$) and the number of themes $Q$ ($1 \leq Q \leq 100,000$). Each of the subsequent $N-1$ lines provides the information regarding the $i$-th road $u_i,v_i,w_i$ ($ 1 \leq u_i < v_i \leq N, 1 \leq w_i \leq 10,000$), indicating that the road connects cities $u_i$ and $v_i$, and the road distance between the two is $w_i$. Each of the $Q$ lines that follows the above provides the three cities assigned to the $i$-th theme: $a_i,b_i,c_i$ ($1 \leq a_i < b_i < c_i \leq N$).

Output

For each theme, output the cost in one line.

Sample Input 1

5 4
1 2 3
2 3 4
2 4 2
4 5 3
1 3 4
1 4 5
1 2 3
2 4 5

Sample Output 1

4
5
4
3

In the first theme, traveling distance from City 3 (the student conducts survey) to City 2 (meeting venue) determines the cost 4. As no other meeting city can provide smaller cost, you should output 4. In the second theme, you can minimize the cost down to 5 by selecting City 2 or City 4 as the meeting venue.

Sample Input 2

5 3
1 2 1
2 3 1
3 4 1
4 5 1
1 2 3
1 3 5
1 2 4

Sample Output 2

1
2
2

Sample Input 3

15 15
1 2 45
2 3 81
1 4 29
1 5 2
5 6 25
4 7 84
7 8 56
4 9 2
4 10 37
7 11 39
1 12 11
11 13 6
3 14 68
2 15 16
10 13 14
13 14 15
2 14 15
7 12 15
10 14 15
9 10 15
9 14 15
8 13 15
5 6 13
11 13 15
12 13 14
2 3 10
5 13 15
10 11 14
6 8 11

Sample Output 3

194
194
97
90
149
66
149
140
129
129
194
111
129
194
140
Party Dress

Yae joins a journey plan, in which parties will be held several times during the itinerary. She wants to participate in all of them and will carry several dresses with her. But the number of dresses she can carry with her may be smaller than that of the party opportunities. In that case, she has to wear some of her dresses more than once.

Fashion-conscious Yae wants to avoid that. At least, she wants to reduce the maximum number of times she has to wear the same dress as far as possible.

Given the number of dresses and frequency of parties, make a program to determine how she can reduce the maximum frequency of wearing the most reused dress.

Input

The input is given in the following format.

$A$ $B$

The input line provides the number of dresses $A$ ($1 \leq A \leq 10^5$) and frequency of parties $B$ ($1 \leq B \leq 10^5$).

Output

Output the frequency she has to wear the most reused dress.

Sample Input 1

3 5

Sample Output 1

2

Sample Input 2

25 10

Sample Output 2

1
Design of a Mansion

Our master carpenter is designing a condominium called Bange Hills Mansion. The condominium is constructed by stacking up floors of the same height. The height of each floor is designed so that the total height of the stacked floors coincides with the predetermined height of the condominium. The height of each floor can be adjusted freely with a certain range.

The final outcome of the building depends on clever height allotment for each floor. So, he plans to calculate possible combinations of per-floor heights to check how many options he has.

Given the height of the condominium and the adjustable range of each floor’s height, make a program to enumerate the number of choices for a floor.

Input

The input is given in the following format.

$H$ $A$ $B$

The input line provides the height of the condominium $H$ ($1 \leq H \leq 10^5$) and the upper and lower limits $A$ and $B$ of the height adjustable range for one floor ($1 \leq A \leq B \leq H$). All data are given as integers.

Output

Output the number of possible height selections for each floor in a line.

Sample Input 1

100 2 4

Sample Output 1

2

Sample Input 2

101 3 5

Sample Output 2

0
Pilling Blocks

We make a tower by stacking up blocks. The tower consists of several stages and each stage is constructed by connecting blocks horizontally. Each block is of the same weight and is tough enough to withstand the weight equivalent to up to $K$ blocks without crushing.

We have to build the tower abiding by the following conditions:

Every stage of the tower has one or more blocks on it.

Each block is loaded with weight that falls within the withstanding range of the block. The weight loaded on a block in a stage is evaluated by: total weight of all blocks above the stage divided by the number of blocks within the stage.

Given the number of blocks and the strength, make a program to evaluate the maximum height (i.e., stages) of the tower than can be constructed.

Input

The input is given in the following format.

$N$ $K$

The input line provides the number of blocks available $N$ ($1 \leq N \leq 10^5$) and the strength of the block $K$ ($1 \leq K \leq 10^5$).

Output

Output the maximum possible number of stages.

Sample Input 1

4 2

Sample Output 1

3

Sample Input 2

5 2

Sample Output 2

4