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

In a certain programming contest, T-shirts are awarded to participants according to the following rules.

• All participants who ranked A-th or higher get a T-shirt.
• Additionally, from the participants who ranked between (A+1)-th and B-th (inclusive), C participants chosen uniformly at random get a T-shirt.

There were 1000 participants in this contest, and all of them got different ranks.
Iroha-chan, who participated in this contest, ranked X-th.
Find the probability that she gets a T-shirt.

Constraints

• All values in input are integers.
• 1 \le A < B \le 1000
• 1 \le C \le B-A
• 1 \le X \le 1000

Sample Input 1

30 500 20 103

Sample Output 1

0.042553191489

Iroha-chan ranked 103-rd.
She will get a T-shirt if she is among the 20 participants chosen uniformly at random from the 470 participants who ranked between 31-st and 500-th, which happens with probability \frac{20}{470}=0.04255319\dots.

Sample Input 2

50 500 100 1

Sample Output 2

1.000000000000

Iroha-chan ranked 1-st. This time, she is guaranteed to get a T-shirt.

Sample Input 3

1 2 1 1000

Sample Output 3

0.000000000000

Iroha-chan ranked 1000-th. This time, she will never get a T-shirt.

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

In this problem, an input file contains multiple test cases.
You are first given an integer T. Solve the following problem for T test cases.

• We have N positive integers A_1, A_2, ..., A_N. How many of them are odd?

Constraints

• 1 \leq T \leq 100
• 1 \leq N \leq 100
• 1 \leq A_i \leq 10^9
• All values in the input are integers.

Sample Input 1

4
3
1 2 3
2
20 23
10
6 10 4 1 5 9 8 6 5 1
1
1000000000

Sample Output 1

2
1
5
0

This input contains four test cases.

The second and third lines correspond to the first test case, where N = 3, A_1 = 1, A_2 = 2, A_3 = 3.
We have two odd numbers in A_1, A_2, and A_3, so the first line should contain 2.

Problem Statement

You are given a positive integer N.

Find the number of triples of positive integers (A, B, C) such that A\leq B\leq C and ABC\leq N.

The Constraints guarantee that the answer is less than 2^{63}.

Constraints

• 1 \leq N \leq 10^{11}
• N is an integer.

Sample Input 1

4

Sample Output 1

5

There are five such triples: (1,1,1),(1,1,2),(1,1,3),(1,1,4),(1,2,2).

Sample Input 2

100

Sample Output 2

323

Sample Input 3

100000000000

Sample Output 3

5745290566750

Problem Statement

As KEYENCE headquarters have more and more workers, they decided to divide the departments in the headquarters into two groups and stagger their lunch breaks.

KEYENCE headquarters have N departments, and the number of people in the i-th department (1\leq i\leq N) is K_i.

When assigning each department to Group A or Group B, having each group take lunch breaks at the same time, and ensuring that the lunch break times of Group A and Group B do not overlap, find the minimum possible value of the maximum number of people taking a lunch break at the same time.
In other words, find the minimum possible value of the larger of the following: the total number of people in departments assigned to Group A, and the total number of people in departments assigned to Group B.

Constraints

• 2 \leq N \leq 20
• 1 \leq K_i \leq 10^8
• All input values are integers.

Sample Input 1

5
2 3 5 10 12

Sample Output 1

17

When assigning departments 1, 2, and 5 to Group A, and departments 3 and 4 to Group B, Group A has a total of 2+3+12=17 people, and Group B has a total of 5+10=15 people. Thus, the maximum number of people taking a lunch break at the same time is 17.

It is impossible to assign the departments so that both groups have 16 or fewer people, so print 17.

Sample Input 2

2
1 1

Sample Output 2

1

Multiple departments may have the same number of people.

Sample Input 3

6
22 25 26 45 22 31

Sample Output 3

89

For example, when assigning departments 1, 4, and 5 to Group A, and departments 2, 3, and 6 to Group B, the maximum number of people taking a lunch break at the same time is 89.

Problem Statement

This is an interactive task, where your program and the judge interact via Standard Input and Output.

The judge has a string of length N consisting of 0 and 1: S = S_1S_2\ldots S_N. Here, S_1 = 0 and S_N = 1.

You are given the length N of S, but not the contents of S. Instead, you can ask the judge at most 20 questions as follows.

• Choose an integer i such that 1 \leq i \leq N and ask the value of S_i.

Print an integer p such that 1 \leq p \leq N-1 and S_p \neq S_{p+1}.
It can be shown that such p always exists under the settings of this problem.

Constraints

• 2 \leq N \leq 2 \times 10^5

Input and Output

First, receive the length N of the string S from Standard Input:

N

Then, you get to ask the judge at most 20 questions as described in the problem statement.

Print each question to Standard Output in the following format, where i is an integer satisfying 1 \leq i \leq N:

? i

In response to this, the value of S_i will be given from Standard Input in the following format:

S_i

Here, S_i is 0 or 1.

When you find an integer p satisfying the condition in the problem statement, print it in the following format, and immediately quit the program:

! p

If multiple solutions exist, you may print any of them.

Notes

• Print a newline and flush Standard Output at the end of each message. Otherwise, you may get a TLE verdict.
• If there is malformed output during the interaction or your program quits prematurely, the verdict will be indeterminate.
• After printing the answer, immediately quit the program. Otherwise, the verdict will be indeterminate.
• The string S will be fixed at the start of the interaction and will not be changed according to your questions or other factors.

Sample Input and Output

In the following interaction, N = 7 and S = 0010011.

For the presented p = 5, we have 1 \leq p \leq N-1 and S_p \neq S_{p+1}. Thus, if the program immediately quits here, this case will be judged as correctly solved.

Problem Statement

You are given a sequence A = (A_1, A_2, \dots, A_N) of length N. For each k = 1, 2, \dots, N, find the number, modulo 998244353, of (not necessarily contiguous) subsequences of A of length k that are arithmetic sequences. Two subsequences are distinguished if they are taken from different positions, even if they are equal as sequences.

Constraints

• 1 \leq N \leq 80
• 1 \leq A_i \leq 10^9
• All input values are integers.

Sample Input 1

5
1 2 3 2 3

Sample Output 1

5 10 3 0 0

• There are 5 subsequences of length 1, all of which are arithmetic sequences.
• There are 10 subsequences of length 2, all of which are arithmetic sequences.
• There are 3 subsequences of length 3 that are arithmetic sequences: (A_1, A_2, A_3), (A_1, A_2, A_5), and (A_1, A_4, A_5).
• There are no arithmetic subsequences of length 4 or more.

Sample Input 2

4
1 2 3 4

Sample Output 2

4 6 2 1

Sample Input 3

1
100

Sample Output 3

1

Problem Statement

For a positive integer x, define f(x) as follows: "While x is even, keep dividing it by 2. The final value of x after these divisions is f(x)." For example, f(4)=f(2)=f(1)=1, and f(12)=f(6)=f(3)=3.

Given an integer sequence A=(A_1,A_2,\ldots,A_N) of length N, find \displaystyle \sum_{i=1}^N \sum_{j=i}^N f(A_i+A_j).

Constraints

• 1\le N\le 2\times 10^5
• 1\le A_i\le 10^7
• All input values are integers.

Sample Input 1

2
4 8

Sample Output 1

5

f(A_1+A_1)=f(8)=1, f(A_1+A_2)=f(12)=3, f(A_2+A_2)=f(16)=1. Thus, Print 1+3+1=5.

Sample Input 2

3
51 44 63

Sample Output 2

384

Sample Input 3

8
577752 258461 183221 889769 278633 577212 392309 326001

Sample Output 3

20241214