Problem Statement

Given a string S, print AC if it perfectly matches Hello,World!; otherwise, print WA.

Constraints

• 1 \le |S| \le 15
• S consists of English lowercase letters, English uppercase letters, ,, and !.

Sample Input 1

Hello,World!

Sample Output 1

AC

The string S perfectly matches Hello,World!.

Sample Input 2

Hello,world!

Sample Output 2

WA

The seventh character from the beginning should be an uppercase W in Hello,World!, but S has a lowercase w in that position. Thus, S does not match Hello,World!.

Sample Input 3

Hello!World!

Sample Output 3

WA

Problem Statement

You are given two different strings S and T.
If S is lexicographically smaller than T, print Yes; otherwise, print No.

Note that many major programming languages implement lexicographical comparison of strings as operators or functions in standard libraries. For more detail, see your language's reference.

Constraints

• S and T are different strings, each of which consists of lowercase English letters and has a length of between 1 and 10 (inclusive).

Sample Input 1

abc atcoder

Sample Output 1

Yes

abc and atcoder begin with the same character, but their second characters are different. Since b comes earlier than t in alphabetical order, we can see that abc is lexicographically smaller than atcoder.

Sample Input 2

arc agc

Sample Output 2

No

Sample Input 3

a aa

Sample Output 3

Yes

Problem Statement

You are given a positive integer N. If there are integers x and y such that N=2^x3^y, print Yes; otherwise, print No.

Constraints

• 1\leq N\leq10^{18}
• N is an integer.

Sample Input 1

324

Sample Output 1

Yes

For x=2,y=4, we have 2^x3^y=2^23^4=4\times81=324, so the condition is satisfied. Thus, you should print Yes.

Sample Input 2

5

Sample Output 2

No

There are no integers x and y such that 2^x3^y=5. Thus, you should print No.

Sample Input 3

32

Sample Output 3

Yes

For x=5,y=0, we have 2^x3^y=32\times1=32, so you should print Yes.

Sample Input 4

37748736

Sample Output 4

Yes

Problem Statement

There are N players numbered 1 to N, who have played a round-robin tournament. For every match in this tournament, one player won and the other lost.

The results of the matches are given as N strings S_1,S_2,\ldots,S_N of length N each, in the following format:

• If i\neq j, the j-th character of S_i is o or x. o means that player i won against player j, and x means that player i lost to player j.

• If i=j, the j-th character of S_i is -.

The player with more wins ranks higher. If two players have the same number of wins, the player with the smaller player number ranks higher. Report the player numbers of the N players in descending order of rank.

Constraints

• 2\leq N\leq 100
• N is an integer.
• S_i is a string of length N consisting of o, x, and -.
• S_1,\ldots,S_N conform to the format described in the problem statement.

Sample Input 1

3
-xx
o-x
oo-

Sample Output 1

3 2 1

Player 1 has 0 wins, player 2 has 1 win, and player 3 has 2 wins. Thus, the player numbers in descending order of rank are 3,2,1.

Sample Input 2

7
-oxoxox
x-xxxox
oo-xoox
xoo-ooo
ooxx-ox
xxxxx-x
oooxoo-

Sample Output 2

4 7 3 1 5 2 6

Both players 4 and 7 have 5 wins, but player 4 ranks higher because their player number is smaller.

Problem Statement

There is a tree T with N vertices. The i-th edge (1\leq i\leq N-1) connects vertex U_i and vertex V_i.

You are given two different vertices X and Y in T. List all vertices along the simple path from vertex X to vertex Y in order, including endpoints.

It can be proved that, for any two different vertices a and b in a tree, there is a unique simple path from a to b.

Constraints

• 1\leq N\leq 2\times 10^5
• 1\leq X,Y\leq N
• X\neq Y
• 1\leq U_i,V_i\leq N
• All values in the input are integers.
• The given graph is a tree.

Sample Input 1

5 2 5
1 2
1 3
3 4
3 5

Sample Output 1

2 1 3 5

The tree T is shown below. The simple path from vertex 2 to vertex 5 is 2 \to 1 \to 3 \to 5.
Thus, 2,1,3,5 should be printed in this order, with spaces in between.

Sample Input 2

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

Sample Output 2

1 2

The tree T is shown below.

Problem Statement

We have an empty box.
Takahashi can cast the following two spells any number of times in any order.

• Spell A: puts one new ball into the box.
• Spell B: doubles the number of balls in the box.

Tell us a way to have exactly N balls in the box with at most \mathbf{120} casts of spells.
It can be proved that there always exists such a way under the Constraints given.

There is no way other than spells to alter the number of balls in the box.

Constraints

• 1 \leq N \leq 10^{18}
• All values in input are integers.

Sample Input 1

5

Sample Output 1

AABA

This changes the number of balls as follows: 0 \xrightarrow{A} 1\xrightarrow{A} 2 \xrightarrow{B}4\xrightarrow{A} 5.
There are also other acceptable outputs, such as AAAAA.

Sample Input 2

14

Sample Output 2

BBABBAAAB

This changes the number of balls as follows: 0 \xrightarrow{B} 0 \xrightarrow{B} 0 \xrightarrow{A}1 \xrightarrow{B} 2 \xrightarrow{B} 4 \xrightarrow{A}5 \xrightarrow{A}6 \xrightarrow{A} 7 \xrightarrow{B}14.
It is not required to minimize the length of S.

Problem Statement

We have an empty sequence A.
Given Q queries, process them in order.
Each query is of one of the following three types.

• 1 x : Insert x to A.

• 2 x k : Among the elements of A that are less than or equal to x, print the k-th largest value. (k is no more than \bf{5})
  If there are less than k elements of A that are less than or equal to x, then print -1.

• 3 x k : Among the elements of A that are greater than or equal to x, print the k-th smallest value. (k is no more than \bf{5})
  If there are less than k elements of A that are greater than or equal to x, then print -1.

Constraints

• 1\leq Q \leq 2\times 10^5
• 1\leq x\leq 10^{18}
• 1\leq k\leq 5
• All values in input are integers.

Sample Input 1

11
1 20
1 10
1 30
1 20
3 15 1
3 15 2
3 15 3
3 15 4
2 100 5
1 1
2 100 5

Sample Output 1

20
20
30
-1
-1
1

After \text{query}_{1,2,3,4} have been processed, we have A=(20,10,30,20).

For \text{query}_{5,6,7}, the elements of A greater than or equal to 15 are (20,30,20).
The 1-st smallest value of them is 20; the 2-nd is 20; the 3-rd is 30.

Problem Statement

There is a simple undirected graph with N vertices numbered 1 through N and M edges numbered 1 through M. Edge i connects vertex u_i and vertex v_i.
Every vertex is painted either red or blue. The color of vertex i is represented by C_i; vertex i is painted red if C_i is 0 and blue if C_i is 1.

Now, Takahashi is on vertex 1 and Aoki is on vertex N.
They may repeat the following move zero or more times.

• Each of the two simultaneously moves to a vertex adjacent to the current vertex.
  Here, the vertices that Takahashi and Aoki move to must have different colors.

By repeating the move above, can Takahashi and Aoki simultaneously end up on vertices N and 1, respectively?
If it is possible, find the minimum number of moves required. If it is impossible, print -1.

You are given T at the beginning of the input. Solve the problem for T test cases.

Constraints

• 1 \leq T \leq 1000
• 2 \leq N \leq 2000
• 1 \leq M \leq \min(\frac{N(N-1)}{2}, 2000)
• C_i \in \lbrace 0, 1 \rbrace
• 1 \leq u_i, v_i \leq N
• The graph given in the input is simple.
• All values in the input are integers.
• The sum of N over all test cases does not exceed 2000.
• The sum of M over all test cases does not exceed 2000.

Sample Input 1

3
4 4
0 1 0 1
1 2
2 3
1 3
2 4
3 3
0 1 0
1 2
2 3
1 3
6 6
0 0 1 1 0 1
1 2
2 6
3 6
4 6
4 5
2 4

Sample Output 1

3
-1
3

For the 1-st test case, Takahashi and Aoki can achieve the objective by making the following 3 moves, which is the minimum number:

• Takahashi moves to vertex 3, and Aoki moves to vertex 2.
• Takahashi moves to vertex 2, and Aoki moves to vertex 3.
• Takahashi moves to vertex 4, and Aoki moves to vertex 1.

Note that in the 1-st move, it is disallowed that both Takahashi and Aoki move to vertex 2 (because the colors of vertices that Takahashi and Aoki move to must be different.)

For the 2-nd case, no matter how they move, they cannot achieve the objective.

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