Problem Statement

In the Kingdom of AtCoder, there is a standardized test of competitive programming proficiency.

An examinee will get a score out of 100 and obtain a rank according to the score, as follows:

• Novice, for a score not less than 0 but less than 40;
• Intermediate, for a score not less than 40 but less than 70;
• Advanced, for a score not less than 70 but less than 90;
• Expert, for a score not less than 90.

Takahashi took this test and got X points.

Find the minimum number of extra points needed to go up one rank higher. If, however, his rank was Expert, print expert, as there is no higher rank than that.

Constraints

• 0 \leq X \leq 100
• X is an integer.

Sample Input 1

56

Sample Output 1

14

He got 56 points and was certified as Intermediate. In order to reach the next rank of Advanced, he needs at least 14 more points.

Sample Input 2

32

Sample Output 2

8

Sample Input 3

0

Sample Output 3

40

Sample Input 4

100

Sample Output 4

expert

He got full points and was certified as Expert. There is no rank higher than that, so print expert.

Problem Statement

You are given a string S of length 3.
Print a character that occurs only once in S.
If there is no such character, print -1 instead.

Constraints

• S is a string of length 3 consisting of lowercase English letters.

Sample Input 1

pop

Sample Output 1

o

o occurs only once in pop.

Sample Input 2

abc

Sample Output 2

a

a, b, and c occur once each in abc, so you may print any of them.

Sample Input 3

xxx

Sample Output 3

-1

No character occurs only once in xxx.

Problem Statement

Given a non-negative integer X, perform the following operation for i=1,2,\dots,K in this order and find the resulting X.

• Round X off to the nearest 10^i.
  • Formally, replace X with Y that is "the largest multiple of 10^i that minimizes |Y-X|."
  • Here are some examples:
    • Rounding 273 off to the nearest 10^2 yields 300.
    • Rounding 999 off to the nearest 10^3 yields 1000.
    • Rounding 100 off to the nearest 10^{10} yields 0.
    • Rounding 1015 off to the nearest 10^1 yields 1020.

Constraints

• X and K are integers.
• 0 \le X < 10^{15}
• 1 \le K \le 15

Sample Input 1

2048 2

Sample Output 1

2100

X changes as 2048 \rightarrow 2050 \rightarrow 2100 by the operations.

Sample Input 2

1 15

Sample Output 2

0

Sample Input 3

999 3

Sample Output 3

1000

Sample Input 4

314159265358979 12

Sample Output 4

314000000000000

X may not fit into a 32-bit integer type.

Problem Statement

You are given two strings S and T. Determine whether it is possible to make S and T equal by doing the following operation at most once:

• choose two adjacent characters in S and swap them.

Note that it is allowed to choose not to do the operation.

Constraints

• Each of S and T is a string of length between 2 and 100 (inclusive) consisting of lowercase English letters.
• S and T have the same length.

Sample Input 1

abc
acb

Sample Output 1

Yes

You can swap the 2-nd and 3-rd characters of S to make S and T equal.

Sample Input 2

aabb
bbaa

Sample Output 2

No

There is no way to do the operation to make S and T equal.

Sample Input 3

abcde
abcde

Sample Output 3

Yes

S and T are already equal.

Problem Statement

There is an N \times N grid, where the cell at the i-th row from the top and the j-th column from the left contains the integer N \times (i-1) + j.

Over T turns, integers will be announced. On Turn i, the integer A_i is announced, and the cell containing A_i is marked. Determine the turn on which Bingo is achieved for the first time. If Bingo is not achieved within T turns, print -1.

Here, achieving Bingo means satisfying at least one of the following conditions:

• There exists a row in which all N cells are marked.
• There exists a column in which all N cells are marked.
• There exists a diagonal line (from top-left to bottom-right or from top-right to bottom-left) in which all N cells are marked.

Constraints

• 2 \leq N \leq 2 \times 10^3
• 1 \leq T \leq \min(N^2, 2 \times 10^5)
• 1 \leq A_i \leq N^2
• A_i \neq A_j if i \neq j.
• All input values are integers.

Sample Input 1

3 5
5 1 8 9 7

Sample Output 1

4

The state of the grid changes as follows. Bingo is achieved for the first time on Turn 4.

Sample Input 2

3 5
4 2 9 7 5

Sample Output 2

-1

Bingo is not achieved within five turns, so print -1.

Sample Input 3

4 12
13 9 6 5 2 7 16 14 8 3 10 11

Sample Output 3

9

Problem Statement

There are N people in an xy-plane. Person i is at (X_i, Y_i). The positions of all people are different.

We have a string S of length N consisting of L and R.
If S_i = R, Person i is facing right; if S_i = L, Person i is facing left. All people simultaneously start walking in the direction they are facing. Here, right and left correspond to the positive and negative x-direction, respectively.

For example, the figure below shows the movement of people when (X_1, Y_1) = (2, 3), (X_2, Y_2) = (1, 1), (X_3, Y_3) =(4, 1), S = RRL.

We say that there is a collision when two people walking in opposite directions come to the same position. Will there be a collision if all people continue walking indefinitely?

Constraints

• 2 \leq N \leq 2 \times 10^5
• 0 \leq X_i \leq 10^9
• 0 \leq Y_i \leq 10^9
• (X_i, Y_i) \neq (X_j, Y_j) if i \neq j.
• All X_i and Y_i are integers.
• S is a string of length N consisting of L and R.

Sample Input 1

3
2 3
1 1
4 1
RRL

Sample Output 1

Yes

This input corresponds to the example in the Problem Statement.
If all people continue walking, Person 2 and Person 3 will collide. Thus, Yes should be printed.

Sample Input 2

2
1 1
2 1
RR

Sample Output 2

No

Since Person 1 and Person 2 walk in the same direction, they never collide.

Sample Input 3

10
1 3
1 4
0 0
0 2
0 4
3 1
2 4
4 2
4 4
3 3
RLRRRLRLRR

Sample Output 3

Yes

Problem Statement

Takahashi found a puzzle along some road.
It is composed of an undirected graph with nine vertices and M edges, and eight pieces.

The nine vertices of the graph are called Vertex 1, Vertex 2, \ldots, Vertex 9. For each i = 1, 2, \ldots, M, the i-th edge connects Vertex u_i and Vertex v_i.
The eight pieces are called Piece 1, Piece 2, \ldots, Piece 8. For each j = 1, 2, \ldots, 8, Piece j is on Vertex p_j.
Here, it is guaranteed that all pieces are on distinct vertices. Note that there is exactly one empty vertex without a piece.

Takahashi can do the following operation on the puzzle any number of times (possibly zero).

Choose a piece on a vertex adjacent to the empty vertex, and move it to the empty vertex.

By repeating this operation, he aims to complete the puzzle. The puzzle is considered complete when the following holds.

• For each j = 1, 2, \ldots, 8, Piece j is on Vertex j.

Determine whether it is possible for Takahashi to complete the puzzle. If it is possible, find the minimum number of operations needed to do so.

Constraints

• 0 \leq M \leq 36
• 1 \leq u_i, v_i \leq 9
• The given graph has no multi-edges or self-loops.
• 1 \leq p_j \leq 9
• j \neq j' \Rightarrow p_j \neq p_{j'}
• All values in input are integers.

Sample Input 1

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

Sample Output 1

5

The following procedure completes the puzzle in five operations.

1. Move Piece 2 from Vertex 9 to Vertex 1.
2. Move Piece 3 from Vertex 2 to Vertex 9.
3. Move Piece 2 from Vertex 1 to Vertex 2.
4. Move Piece 1 from Vertex 3 to Vertex 1.
5. Move Piece 3 from Vertex 9 to Vertex 3.

On the other hand, it is impossible to complete the puzzle in less than five operations. Thus, we should print 5.
Note that the given graph may not be connected.

Sample Input 2

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

Sample Output 2

0

The puzzle is already complete from the beginning. Thus, the minimum number of operations needed to complete the puzzle is 0.

Sample Input 3

12
8 5
9 6
4 5
4 1
2 5
8 9
2 1
3 6
8 7
6 5
7 4
2 3
1 2 3 4 5 6 8 7

Sample Output 3

-1

No sequence of operations can complete the puzzle, so we should print -1.

Sample Input 4

12
6 5
5 4
4 1
4 7
8 5
2 1
2 5
6 9
3 6
9 8
8 7
3 2
2 3 4 6 1 9 7 8

Sample Output 4

16

Problem Statement

There are N integers a_1,\ldots,a_N written on a whiteboard.
Here, a_i can be represented as a_i = p_{i,1}^{e_{i,1}} \times \ldots \times p_{i,m_i}^{e_{i,m_i}} using m_i prime numbers p_{i,1} \lt \ldots \lt p_{i,m_i} and positive integers e_{i,1},\ldots,e_{i,m_i}.
You will choose one of the N integers to replace it with 1.
Find the number of values that can be the least common multiple of the N integers after the replacement.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq m_i
• \sum{m_i} \leq 2 \times 10^5
• 2 \leq p_{i,1} \lt \ldots \lt p_{i,m_i} \leq 10^9
• p_{i,j} is prime.
• 1 \leq e_{i,j} \leq 10^9
• All values in input are integers.

Sample Input 1

4
1
7 2
2
2 2
5 1
1
5 1
2
2 1
7 1

Sample Output 1

3

The integers on the whiteboard are a_1 =7^2=49, a_2=2^2 \times 5^1 = 20, a_3 = 5^1 = 5, a_4=2^1 \times 7^1 = 14.
If you replace a_1 with 1, the integers on the whiteboard become 1,20,5,14, whose least common multiple is 140.
If you replace a_2 with 1, the integers on the whiteboard become 49,1,5,14, whose least common multiple is 490.
If you replace a_3 with 1, the integers on the whiteboard become 49,20,1,14, whose least common multiple is 980.
If you replace a_4 with 1, the integers on the whiteboard become 49,20,5,1, whose least common multiple is 980.
Therefore, the least common multiple of the N integers after the replacement can be 140, 490, or 980, so the answer is 3.

Sample Input 2

1
1
998244353 1000000000

Sample Output 2

1

There may be enormous integers on the whiteboard.

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