Problem Statement

You are given a 6-digit positive integer N.
Determine whether N satisfies all of the following conditions.

• Among the digits of N, the digit 1 appears exactly once.
• Among the digits of N, the digit 2 appears exactly twice.
• Among the digits of N, the digit 3 appears exactly three times.

Constraints

• N is an integer satisfying 100000 \le N \le 999999.

Sample Input 1

123233

Sample Output 1

Yes

123233 satisfies the conditions in the problem statement, so print Yes.

Sample Input 2

123234

Sample Output 2

No

123234 does not satisfy the conditions in the problem statement, so print No.

Sample Input 3

323132

Sample Output 3

Yes

Sample Input 4

500000

Sample Output 4

No

Problem Statement

You are given a sequence P that is a permutation of (1,2,…,N), and an integer X. The i-th term of P has a value of P_i. Print k such that P_k = X.

Constraints

• 1 \leq N \leq 100
• 1 \leq X \leq N
• P is a permutation of (1,2,…,N).
• All values in the input are integers.

Sample Input 1

4 3
2 3 1 4

Sample Output 1

2

We have P = (2,3,1,4), so P_2 = 3. Thus, you should print 2.

Sample Input 2

5 2
3 5 1 4 2

Sample Output 2

5

Sample Input 3

6 6
1 2 3 4 5 6

Sample Output 3

6

Problem Statement

We define Extended A strings, Extended B strings, Extended C strings, and Extended ABC strings as follows:

• A string S is an Extended A string if all characters in S are A.
• A string S is an Extended B string if all characters in S are B.
• A string S is an Extended C string if all characters in S are C.
• A string S is an Extended ABC string if there is an Extended A string S_A, an Extended B string S_B, and an Extended C string S_C such that the string obtained by concatenating S_A, S_B, S_C in this order equals S.

For example, ABC, A, and AAABBBCCCCCCC are Extended ABC strings, but ABBAAAC and BBBCCCCCCCAAA are not. Note that the empty string is an Extended A string, an Extended B string, and an Extended C string.

You are given a string S consisting of A, B, and C. If S is an Extended ABC string, print Yes; otherwise, print No.

Constraints

• S is a string consisting of A, B, and C.
• 1\leq|S|\leq 100 (|S| is the length of the string S.)

Sample Input 1

AAABBBCCCCCCC

Sample Output 1

Yes

AAABBBCCCCCCC is an Extended ABC string because it is a concatenation of an Extended A string of length 3, AAA, an Extended B string of length 3, BBB, and an Extended C string of length 7, CCCCCCC, in this order.

Thus, print Yes.

Sample Input 2

ACABABCBC

Sample Output 2

No

There is no triple of Extended A string S_A, Extended B string S_B, and Extended C string S_C such that the string obtained by concatenating S_A, S_B, and S_C in this order equals ACABABCBC.

Therefore, print No.

Sample Input 3

A

Sample Output 3

Yes

Sample Input 4

ABBBBBBBBBBBBBCCCCCC

Sample Output 4

Yes

Problem Statement

Note: This problem has almost the same setting as Problem F. Only the parts in bold in the main text and constraints differ.

You are holding a ring with both hands. This ring consists of N\ (N \geq 3) parts numbered 1,2,\dots,N, where parts i and i+1 (1 \leq i \leq N-1) are adjacent, and parts 1 and N are also adjacent.

Initially, your left hand is holding part 1, and your right hand is holding part 2. In one operation, you can do the following:

• Move one of your hands to an adjacent part of the part it is currently holding. However, you can do this only if the other hand is not on the destination part.

The following figure shows the initial state and examples of operations that can and cannot be made from there. The number written on each part of the ring represents the part number, and the circles labeled L and R represent your left and right hands, respectively.

You need to follow Q instructions given to you in order. The i-th (1 \leq i \leq Q) instruction is represented by a character H_i and an integer T_i, meaning the following:

• Perform some number of operations (possibly zero) so that your left hand (if H_i is L) or your right hand (if H_i is R) is holding part T_i. Here, you must not move the other hand not specified by H_i.

It is guaranteed that only achievable instructions are given.

Find the minimum total number of operations required to follow all the instructions.

Constraints

• 3 \leq N \leq 100
• 1 \leq Q \leq 100
• H_i is L or R.
• 1 \leq T_i \leq N
• N, Q, and T_i are integers.
• Only achievable instructions are given (see the problem statement for details).

Sample Input 1

6 3
R 4
L 5
R 6

Sample Output 1

8

By performing the following operations, you can follow all Q instructions in order.

1. Move your right hand as part 2 \rightarrow 3 \rightarrow 4 to follow the first instruction.
2. Move your left hand as part 1 \rightarrow 6 \rightarrow 5 to follow the second instruction.
3. Move your right hand as part 4 \rightarrow 3 \rightarrow 2 \rightarrow 1 \rightarrow 6 to follow the third instruction.

In this case, the total number of operations is 2+2+4=8, which is the minimum. (Note that when following the third instruction, you cannot move your right hand as part 4 \rightarrow 5 \rightarrow 6.)

Sample Input 2

100 2
L 1
R 2

Sample Output 2

0

There are cases where you can follow the instructions without performing any operations.

Sample Input 3

30 8
R 23
R 26
R 29
L 20
R 29
R 19
L 7
L 16

Sample Output 3

92

Problem Statement

There are N types of chemicals 1,2,\dots,N. Your goal is to create a state where all of them are mixed.
You are given a string S of length 2^N-1 consisting of 0 and 1, which represents the following information:

• First, define state i (1 \le i \le 2^N-1) where one or more types of chemicals are mixed as follows:
  • When the k-th digit (1 \le k \le N) from the bottom in the binary representation of i is 1, and only then, chemical k is included.
  • For example, 13 in binary is 1101_{(2)}, so state 13 represents a state where chemicals 1,3,4 are mixed.
• When the i-th character of S is 0, state i is safe.
• When the i-th character of S is 1, state i is dangerous.

You mix chemicals using the following operation:

• First, prepare an empty bottle.
• Next, repeat the following:
  • Choose one type of chemical that has not yet been poured into the bottle and pour it into the bottle.
  • At this time, the chemicals mixed in the bottle must not be in a dangerous state.

Determine whether this operation can create a state where all chemicals are mixed.

You are given T test cases; solve each of them.

Constraints

• T is an integer between 1 and 40000, inclusive.
• N is an integer between 1 and 18, inclusive.
• S is a string of length 2^N-1 consisting of 0 and 1.
• The sum of |S| = 2^N-1 in each input does not exceed 5 \times 10^5.

Sample Input 1

5
3
0010000
3
0010110
1
1
2
100
4
001110010101110

Sample Output 1

Yes
No
No
Yes
Yes

This input contains five test cases.

The 1st case is as follows:

• There are three types of chemicals.
• Only state 3 where chemicals 1,2 are mixed is dangerous, and the other states are safe.
• For example, you can create a state where all chemicals are mixed with the following procedure:
  • First, pour chemical 2 into the bottle. Only chemical 2 is mixed in the bottle, which is state 2, so it is safe.
  • Next, pour chemical 3 into the bottle. Chemicals 2,3 are mixed in the bottle, which is state 6, so it is safe.
  • Finally, pour chemical 1 into the bottle. Chemicals 1,2,3 are mixed in the bottle, which is state 7, so it is safe.

The 2nd case is as follows:

• There are three types of chemicals.
• State 3 where chemicals 1,2 are mixed, state 5 where chemicals 1,3 are mixed, and state 6 where chemicals 2,3 are mixed are dangerous, and the other states are safe.
• For this case, it is impossible to create a state where all chemicals are mixed.

The 3rd case is as follows:

• There is one type of chemical.
• Since state 1 where only chemical 1 is mixed is dangerous, it is impossible to create a state where all chemicals are mixed.