Problem Statement

You are given a string S consisting of lowercase English letters and |. S is guaranteed to contain exactly two |s.

Remove the characters between the two |s, including the |s themselves, and print the resulting string.

Constraints

• S is a string of length between 2 and 100, inclusive, consisting of lowercase English letters and |.
• S contains exactly two |s.

Sample Input 1

atcoder|beginner|contest

Sample Output 1

atcodercontest

Remove all the characters between the two |s and print the result.

Sample Input 2

|spoiler|

Sample Output 2

It is possible that all characters are removed.

Sample Input 3

||xyz

Sample Output 3

xyz

Problem Statement

You are given an integer sequence of length N: A = (A_1,A_2,\ldots,A_N).

Determine whether there is a place in A where the same element appears three or more times in a row.

More formally, determine whether there exists an integer i with 1 \le i \le N-2 such that A_i = A_{i+1} = A_{i+2}.

Constraints

• 3 \le N \le 100
• 1 \le A_i \le 100
• All input values are integers.

Sample Input 1

5
1 4 4 4 2

Sample Output 1

Yes

We have A=(1,4,4,4,2). There is a place where 4 appears three times in a row, so print Yes.

Sample Input 2

6
2 4 4 2 2 4

Sample Output 2

No

We have A=(2,4,4,2,2,4). There is no place where the same element appears three or more times in a row, so print No.

Sample Input 3

8
1 4 2 5 7 7 7 2

Sample Output 3

Yes

Sample Input 4

10
1 2 3 4 5 6 7 8 9 10

Sample Output 4

No

Sample Input 5

13
1 1 1 1 1 1 1 1 1 1 1 1 1

Sample Output 5

Yes

Problem Statement

An election is taking place.

N people voted. The i-th person (1 \leq i \leq N) cast a vote to the candidate named S_i.

Find the name of the candidate who received the most votes. The given input guarantees that there is a unique candidate with the most votes.

Constraints

• 1 \leq N \leq 100
• S_i is a string of length between 1 and 10 (inclusive) consisting of lowercase English letters.
• N is an integer.
• There is a unique candidate with the most votes.

Sample Input 1

5
snuke
snuke
takahashi
takahashi
takahashi

Sample Output 1

takahashi

takahashi got 3 votes, and snuke got 2, so we print takahashi.

Sample Input 2

5
takahashi
takahashi
aoki
takahashi
snuke

Sample Output 2

takahashi

Sample Input 3

1
a

Sample Output 3

a

Problem Statement

You are given a string S consisting of lowercase and uppercase English letters. The length of S is odd.
If the number of uppercase letters in S is greater than the number of lowercase letters, convert all lowercase letters in S to uppercase.
Otherwise, convert all uppercase letters in S to lowercase.

Constraints

• S is a string consisting of lowercase and uppercase English letters.
• The length of S is an odd number between 1 and 99, inclusive.

Sample Input 1

AtCoder

Sample Output 1

atcoder

The string AtCoder contains five lowercase letters and two uppercase letters. Thus, convert all uppercase letters in AtCoder to lowercase, which results in atcoder.

Sample Input 2

SunTORY

Sample Output 2

SUNTORY

The string SunTORY contains two lowercase letters and five uppercase letters. Thus, convert all lowercase letters in SunTORY to uppercase, which results in SUNTORY.

Sample Input 3

a

Sample Output 3

a

Problem Statement

You are given a sequence of N numbers: A=(A_1,\ldots,A_N).

Determine whether there is a pair (i,j) with 1\leq i,j \leq N such that A_i-A_j=X.

Constraints

• 2 \leq N \leq 2\times 10^5
• -10^9 \leq A_i \leq 10^9
• -10^9 \leq X \leq 10^9
• All values in the input are integers.

Sample Input 1

6 5
3 1 4 1 5 9

Sample Output 1

Yes

We have A_6-A_3=9-4=5.

Sample Input 2

6 -4
-2 -7 -1 -8 -2 -8

Sample Output 2

No

There is no pair (i,j) such that A_i-A_j=-4.

Sample Input 3

2 0
141421356 17320508

Sample Output 3

Yes

We have A_1-A_1=0.

Problem Statement

There are N buildings arranged in a line at equal intervals. The height of the i-th building from the front is H_i.

You want to decorate some of these buildings with illuminations so that both of the following conditions are satisfied:

• The chosen buildings all have the same height.
• The chosen buildings are arranged at equal intervals.

What is the maximum number of buildings you can choose? If you choose exactly one building, it is considered to satisfy the conditions.

Constraints

• 1 \leq N \leq 3000
• 1 \leq H_i \leq 3000
• All input values are integers.

Sample Input 1

8
5 7 5 7 7 5 7 7

Sample Output 1

3

Choosing the 2nd, 5th, and 8th buildings from the front satisfies the conditions.

Sample Input 2

10
100 200 300 400 500 600 700 800 900 1000

Sample Output 2

1

Choosing just one building is considered to satisfy the conditions.

Sample Input 3

32
3 1 4 1 5 9 2 6 5 3 5 8 9 7 9 3 2 3 8 4 6 2 6 4 3 3 8 3 2 7 9 5

Sample Output 3

3

Problem Statement

You are given a sequence A = (A_1, A_2, \dots, A_N) of length N consisting of positive integers, and integers x and y.
Determine whether it is possible to place N+1 points p_1, p_2, \dots, p_N, p_{N+1} in the xy-coordinate plane to satisfy all of the following conditions. (It is allowed to place two or more points at the same coordinates.)

• p_1 = (0, 0).
• p_2 = (A_1, 0).
• p_{N+1} = (x, y).
• The distance between the points p_i and p_{i+1} is A_i. (1 \leq i \leq N)
• The segments p_i p_{i+1} and p_{i+1} p_{i+2} form a 90 degree angle. (1 \leq i \leq N - 1)

Constraints

• 2 \leq N \leq 10^3
• 1 \leq A_i \leq 10
• |x|, |y| \leq 10^4
• All values in the input are integers.

Sample Input 1

3 -1 1
2 1 3

Sample Output 1

Yes

The figure below shows a placement where p_1 = (0, 0), p_2 = (2, 0), p_3 = (2, 1), and p_4 = (-1, 1). All conditions in the Problem Statement are satisfied.

Sample Input 2

5 2 0
2 2 2 2 2

Sample Output 2

Yes

Letting p_1 = (0, 0), p_2 = (2, 0), p_3 = (2, 2), p_4 = (0, 2), p_5 = (0, 0), and p_6 = (2, 0) satisfies all the conditions. Note that multiple points may be placed at the same coordinates.

Sample Input 3

4 5 5
1 2 3 4

Sample Output 3

No

Sample Input 4

3 2 7
2 7 4

Sample Output 4

No

Sample Input 5

10 8 -7
6 10 4 1 5 9 8 6 5 1

Sample Output 5

Yes

Problem Statement

In a coordinate space, we want to place three cubes with a side length of 7 so that the volumes of the regions contained in exactly one, two, three cube(s) are V_1, V_2, V_3, respectively.

For three integers a, b, c, let C(a,b,c) denote the cubic region represented by (a\leq x\leq a+7) \land (b\leq y\leq b+7) \land (c\leq z\leq c+7).

Determine whether there are nine integers a_1, b_1, c_1, a_2, b_2, c_2, a_3, b_3, c_3 that satisfy all of the following conditions, and find one such tuple if it exists.

• |a_1|, |b_1|, |c_1|, |a_2|, |b_2|, |c_2|, |a_3|, |b_3|, |c_3| \leq 100
• Let C_i = C(a_i, b_i, c_i)\ (i=1,2,3).
  • The volume of the region contained in exactly one of C_1, C_2, C_3 is V_1.
  • The volume of the region contained in exactly two of C_1, C_2, C_3 is V_2.
  • The volume of the region contained in all of C_1, C_2, C_3 is V_3.

Constraints

• 0 \leq V_1, V_2, V_3 \leq 3 \times 7^3
• All input values are integers.

Sample Input 1

840 84 7

Sample Output 1

Yes
0 0 0 0 6 0 6 0 0

Consider the case (a_1, b_1, c_1, a_2, b_2, c_2, a_3, b_3, c_3) = (0, 0, 0, 0, 6, 0, 6, 0, 0).

The figure represents the positional relationship of C_1, C_2, and C_3, corresponding to the orange, cyan, and green cubes, respectively.

Here,

• All of |a_1|, |b_1|, |c_1|, |a_2|, |b_2|, |c_2|, |a_3|, |b_3|, |c_3| are not greater than 100.
• The region contained in all of C_1, C_2, C_3 is (6\leq x\leq 7)\land (6\leq y\leq 7) \land (0\leq z\leq 7), with a volume of (7-6)\times(7-6)\times(7-0)=7.
• The region contained in exactly two of C_1, C_2, C_3 is ((0\leq x < 6)\land (6\leq y\leq 7) \land (0\leq z\leq 7))\lor((6\leq x\leq 7)\land (0\leq y < 6) \land (0\leq z\leq 7)), with a volume of (6-0)\times(7-6)\times(7-0)\times 2=84.
• The region contained in exactly one of C_1, C_2, C_3 has a volume of 840.

Thus, all conditions are satisfied.

(a_1, b_1, c_1, a_2, b_2, c_2, a_3, b_3, c_3) = (-10, 0, 0, -10, 0, 6, -10, 6, 1) also satisfies all conditions and would be a valid output.

Sample Input 2

343 34 3

Sample Output 2

No

No nine integers a_1, b_1, c_1, a_2, b_2, c_2, a_3, b_3, c_3 satisfy all of the conditions.

Problem Statement

You are given a directed graph with N vertices and M edges. The vertices are numbered 1 through N, and the edges are numbered 1 through M. Edge i (1 \leq i \leq M) goes from Vertex s_i to Vertex t_i and has a length of 1.

For each i (1 \leq i \leq M), find the shortest distance from Vertex 1 to Vertex N when all edges except Edge i are passable, or print -1 if Vertex N is unreachable from Vertex 1.

Constraints

• 2 \leq N \leq 400
• 1 \leq M \leq N(N-1)
• 1 \leq s_i,t_i \leq N
• s_i \neq t_i
• (s_i,t_i) \neq (s_j,t_j) (i \neq j)
• All values in input are integers.

Sample Input 1

3 3
1 2
1 3
2 3

Sample Output 1

1
2
1

Sample Input 2

4 4
1 2
2 3
2 4
3 4

Sample Output 2

-1
2
3
2

Vertex N is unreachable from Vertex 1 when all edges except Edge 1 are passable, so the corresponding line contains -1.

Sample Input 3

5 10
1 2
1 4
1 5
2 1
2 3
3 1
3 2
3 5
4 2
4 3

Sample Output 3

1
1
3
1
1
1
1
1
1
1

Sample Input 4

4 1
1 2

Sample Output 4

-1