Problem Statement

You are given a string S consisting of lowercase English letters.

Swap the a-th and b-th characters from the beginning of S and print the resulting string.

Constraints

• S is a string consisting of lowercase English letters.
• The length of S, |S|, satisfies 2 \leq |S| \leq 10.
• 1 \leq a < b \leq |S|
• a and b are integers.

Sample Input 1

chokudai
3 5

Sample Output 1

chukodai

After swapping the 3-rd character o and 5-th character u of chokudai, we have chukodai.

Sample Input 2

aa
1 2

Sample Output 2

aa

In this sample, after swapping the 1-st and 2-nd characters of S, we have the same string as S.

Sample Input 3

aaaabbbb
1 8

Sample Output 3

baaabbba

Problem Statement

There are N people numbered 1 through N. Each person has a integer score called programming ability; person i's programming ability is P_i points. How many more points does person 1 need, so that person 1 becomes the strongest? In other words, what is the minimum non-negative integer x such that P_1 + x > P_i for all i \neq 1?

Constraints

• 1\leq N \leq 100
• 1\leq P_i \leq 100
• All input values are integers.

Sample Input 1

4
5 15 2 10

Sample Output 1

11

Person 1 becomes the strongest when their programming skill is 16 points or more, so the answer is 16-5=11.

Sample Input 2

4
15 5 2 10

Sample Output 2

0

Person 1 is already the strongest, so no more programming skill is needed.

Sample Input 3

3
100 100 100

Sample Output 3

1

Problem Statement

N players numbered 1 to N will play a soccer game.
When a player commits an offense, that player will receive a yellow card or a red card.
A player who satisfies one of the following conditions will be removed from the game.

• Accumulates two yellow cards.
• Receives a red card.

Once a player is removed, that player will no longer receive any cards.

You will watch this game. Initially, the players have not received any cards.
There will be Q events. Correctly answer the questions asked in the events.
There are three kinds of events, which are given in the format c x from the input, where c is 1, 2, or 3. The events are as follows.

• 1 x: Player x receives a yellow card.
• 2 x: Player x receives a red card.
• 3 x: You are asked whether player x has been removed from the game. Answer Yes or No.

Constraints

• 1 \leq N \leq 100
• 1 \leq Q \leq 100
• 1 \leq x \leq N in all events.
• There is at least one event of the third kind.
• A player who has been removed will no longer receive any cards.
• All values in the input are integers.

Sample Input 1

3 9
3 1
3 2
1 2
2 1
3 1
3 2
1 2
3 2
3 3

Sample Output 1

No
No
Yes
No
Yes
No

Here are all the events in chronological order.

In the 1-st event, you are asked whether player 1 has been removed from the game. Player 1 has not been removed, so you should print No.
In the 2-nd event, you are asked whether player 2 has been removed from the game. Player 2 has not been removed, so you should print No.
In the 3-rd event, player 2 receives a yellow card.
In the 4-th event, player 1 receives a red card and is removed from the game.
In the 5-th event, you are asked whether player 1 has been removed from the game. Player 1 has been removed, so you should print Yes.
In the 6-th event, you are asked whether player 2 has been removed from the game. Player 2 has not been removed, so you should print No.
In the 7-th event, player 2 receives a yellow card and is removed from the game.
In the 8-th event, you are asked whether player 2 has been removed from the game. Player 2 has been removed, so you should print Yes.
In the 9-th event, you are asked whether player 3 has been removed from the game. Player 3 has not been removed, so you should print No.

Problem Statement

Takahashi has N teeth, one in each of the holes numbered 1, 2, \dots, N.
Dentist Aoki will perform Q treatments on these teeth and holes.
In the i-th treatment, hole T_i is treated as follows:

• If there is a tooth in hole T_i, remove the tooth from hole T_i.
• If there is no tooth in hole T_i (i.e., the hole is empty), grow a tooth in hole T_i.

After all treatments are completed, how many teeth does Takahashi have?

Constraints

• All input values are integers.
• 1 \le N, Q \le 1000
• 1 \le T_i \le N

Sample Input 1

30 6
2 9 18 27 18 9

Sample Output 1

28

Initially, Takahashi has 30 teeth, and Aoki performs six treatments.

• In the first treatment, hole 2 is treated. There is a tooth in hole 2, so it is removed.
• In the second treatment, hole 9 is treated. There is a tooth in hole 9, so it is removed.
• In the third treatment, hole 18 is treated. There is a tooth in hole 18, so it is removed.
• In the fourth treatment, hole 27 is treated. There is a tooth in hole 27, so it is removed.
• In the fifth treatment, hole 18 is treated. There is no tooth in hole 18, so a tooth is grown.
• In the sixth treatment, hole 9 is treated. There is no tooth in hole 9, so a tooth is grown.

The final count of teeth is 28.

Sample Input 2

1 7
1 1 1 1 1 1 1

Sample Output 2

0

Sample Input 3

9 20
9 5 1 2 2 2 8 9 2 1 6 2 6 5 8 7 8 5 9 8

Sample Output 3

5

Problem Statement

This problem is an easier version of Problem G.

There is a slot machine with three reels.
The arrangement of symbols on the i-th reel is represented by the string S_i. Here, S_i is a string of length M consisting of digits.

Each reel has a corresponding button. For each non-negative integer t, Takahashi can either choose and press one button or do nothing exactly t seconds after the reels start spinning.
If he presses the button corresponding to the i-th reel exactly t seconds after the reels start spinning, the i-th reel will stop and display the ((t \bmod M)+1)-th character of S_i.
Here, t \bmod M denotes the remainder when t is divided by M.

Takahashi wants to stop all the reels so that all the displayed characters are the same.
Find the minimum possible number of seconds from the start of the spin until all the reels are stopped so that his goal is achieved.
If this is impossible, report that fact.

Constraints

• 1 \leq M \leq 100
• M is an integer.
• S_i is a string of length M consisting of digits.

Sample Input 1

10
1937458062
8124690357
2385760149

Sample Output 1

6

Takahashi can stop each reel as follows so that 6 seconds after the reels start spinning, all the reels display 8.

• Press the button corresponding to the second reel 0 seconds after the reels start spinning. The second reel stops and displays 8, the ((0 \bmod 10)+1=1)-st character of S_2.
• Press the button corresponding to the third reel 2 seconds after the reels start spinning. The third reel stops and displays 8, the ((2 \bmod 10)+1=3)-rd character of S_3.
• Press the button corresponding to the first reel 6 seconds after the reels start spinning. The first reel stops and displays 8, the ((6 \bmod 10)+1=7)-th character of S_1.

There is no way to make the reels display the same character in 5 or fewer seconds, so print 6.

Sample Input 2

20
01234567890123456789
01234567890123456789
01234567890123456789

Sample Output 2

20

Note that he must stop all the reels and make them display the same character.

Sample Input 3

5
11111
22222
33333

Sample Output 3

-1

It is impossible to stop the reels so that all the displayed characters are the same.
In this case, print -1.

Problem Statement

A positive integer x is called a 321-like Number when it satisfies the following condition. This definition is the same as the one in Problem A.

• The digits of x are strictly decreasing from top to bottom.
• In other words, if x has d digits, it satisfies the following for every integer i such that 1 \le i < d:
  • (the i-th digit from the top of x) > (the (i+1)-th digit from the top of x).

Note that all one-digit positive integers are 321-like Numbers.

For example, 321, 96410, and 1 are 321-like Numbers, but 123, 2109, and 86411 are not.

Find the K-th smallest 321-like Number.

Constraints

• All input values are integers.
• 1 \le K
• At least K 321-like Numbers exist.

Sample Input 1

15

Sample Output 1

32

The 321-like Numbers are (1,2,3,4,5,6,7,8,9,10,20,21,30,31,32,40,\dots) from smallest to largest.
The 15-th smallest of them is 32.

Sample Input 2

321

Sample Output 2

9610

Sample Input 3

777

Sample Output 3

983210

Problem Statement

Given is a string S consisting of X and ..

You can do the following operation on S between 0 and K times (inclusive).

• Replace a . with an X.

What is the maximum possible number of consecutive Xs in S after the operations?

Constraints

• 1 \leq |S| \leq 2 \times 10^5
• Each character of S is X or ..
• 0 \leq K \leq 2 \times 10^5
• K is an integer.

Sample Input 1

XX...X.X.X.
2

Sample Output 1

5

After replacing the Xs at the 7-th and 9-th positions with X, we have XX...XXXXX., which has five consecutive Xs at 6-th through 10-th positions.
We cannot have six or more consecutive Xs, so the answer is 5.

Sample Input 2

XXXX
200000

Sample Output 2

4

It is allowed to do zero operations.

Problem Statement

There is a circular cake that has been cut into N equal slices by its radii.

Each piece is labeled with an integer from 1 to N in clockwise order, and for each integer i with 1 \leq i \leq N, the piece i is also referred to as piece N + i.

Initially, every piece’s color is color 0.

You can perform the following operation any number of times:

• Choose integers a, b, and c such that 1 \leq a, b, c \leq N. For each integer i with 0 \leq i < b, change the color of piece a + i to color c. The cost of this operation is b + X_c.

You want each piece i (for 1 \leq i \leq N) to have color C_i. Find the minimum total cost of operations needed to achieve this.

Constraints

• 1 \leq N \leq 400
• 1 \leq C_i \leq N
• 1 \leq X_i \leq 10^9
• All input values are integers.

Sample Input 1

6
1 4 2 1 2 5
1 2 3 4 5 6

Sample Output 1

20

Let A_i denote the color of piece i. Initially, (A_1, A_2, A_3, A_4, A_5, A_6) = (0, 0, 0, 0, 0, 0).

Performing an operation with (a, b, c) = (2, 1, 4) changes (A_1, A_2, A_3, A_4, A_5, A_6) to (0, 4, 0, 0, 0, 0).

Performing an operation with (a, b, c) = (3, 3, 2) changes (A_1, A_2, A_3, A_4, A_5, A_6) to (0, 4, 2, 2, 2, 0).

Performing an operation with (a, b, c) = (1, 1, 1) changes (A_1, A_2, A_3, A_4, A_5, A_6) to (1, 4, 2, 2, 2, 0).

Performing an operation with (a, b, c) = (4, 1, 1) changes (A_1, A_2, A_3, A_4, A_5, A_6) to (1, 4, 2, 1, 2, 0).

Performing an operation with (a, b, c) = (6, 1, 5) changes (A_1, A_2, A_3, A_4, A_5, A_6) to (1, 4, 2, 1, 2, 5).

In this case, the total cost is 5 + 5 + 2 + 2 + 6 = 20.

Sample Input 2

5
1 2 3 4 5
1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 2

5000000005

Sample Input 3

8
2 3 3 1 2 1 3 1
3 4 1 2 5 3 1 2

Sample Output 3

23