Problem Statement

You are given two strings S and T consisting of lowercase English letters. Determine if S is a prefix of T.

Constraints

• S and T are strings of lengths between 1 and 100 (inclusive) consisting of lowercase English letters.

Sample Input 1

atco
atcoder

Sample Output 1

Yes

atco is a prefix of atcoder. Thus, Yes should be printed.

Sample Input 2

code
atcoder

Sample Output 2

No

code is not a prefix of atcoder. Thus, No should be printed.

Sample Input 3

abc
abc

Sample Output 3

Yes

Note that a string is also a prefix of itself.

Sample Input 4

aaaa
aa

Sample Output 4

No

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 have an empty sequence and N balls. The size of the i-th ball (1 \leq i \leq N) is 2^{A_i}.

You will perform N operations.
In the i-th operation, you add the i-th ball to the right end of the sequence, and repeat the following steps:

1. If the sequence has one or fewer balls, end the operation.
2. If the rightmost ball and the second rightmost ball in the sequence have different sizes, end the operation.
3. If the rightmost ball and the second rightmost ball in the sequence have the same size, remove these two balls and add a new ball to the right end of the sequence with a size equal to the sum of the sizes of the two removed balls. Then, go back to step 1 and repeat the process.

Determine the number of balls remaining in the sequence after the N operations.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 0 \leq A_i \leq 10^9
• All input values are integers.

Sample Input 1

7
2 1 1 3 5 3 3

Sample Output 1

3

The operations proceed as follows:

• After the first operation, the sequence has one ball, of size 2^2.
• After the second operation, the sequence has two balls, of sizes 2^2 and 2^1 in order.
• After the third operation, the sequence has one ball, of size 2^3. This is obtained as follows:
  • When the third ball is added during the third operation, the sequence has balls of sizes 2^2, 2^1, 2^1 in order.
  • The first and second balls from the right have the same size, so these balls are removed, and a ball of size 2^1 + 2^1 = 2^2 is added. Now, the sequence has balls of sizes 2^2, 2^2.
  • Again, the first and second balls from the right have the same size, so these balls are removed, and a ball of size 2^2 + 2^2 = 2^3 is added, leaving the sequence with a ball of size 2^3.
• After the fourth operation, the sequence has one ball, of size 2^4.
• After the fifth operation, the sequence has two balls, of sizes 2^4 and 2^5 in order.
• After the sixth operation, the sequence has three balls, of sizes 2^4, 2^5, 2^3 in order.
• After the seventh operation, the sequence has three balls, of sizes 2^4, 2^5, 2^4 in order.

Therefore, you should print 3, the final number of balls in the sequence.

Sample Input 2

5
0 0 0 1 2

Sample Output 2

4

The operations proceed as follows:

• After the first operation, the sequence has one ball, of size 2^0.
• After the second operation, the sequence has one ball, of size 2^1.
• After the third operation, the sequence has two balls, of sizes 2^1 and 2^0 in order.
• After the fourth operation, the sequence has three balls, of sizes 2^1, 2^0, 2^1 in order.
• After the fifth operation, the sequence has four balls, of sizes 2^1, 2^0, 2^1, 2^2 in order.

Therefore, you should print 4, the final number of balls in the sequence.

Problem Statement

There are N people, each of whom is either a child or an adult. The i-th person has a weight of W_i.
Whether each person is a child or an adult is specified by a string S of length N consisting of 0 and 1.
If the i-th character of S is 0, then the i-th person is a child; if it is 1, then the i-th person is an adult.

When Takahashi the robot is given a real number X, Takahashi judges a person with a weight less than X to be a child and a person with a weight more than or equal to X to be an adult.
For a real value X, let f(X) be the number of people whom Takahashi correctly judges whether they are children or adults.

Find the maximum value of f(X) for all real values of X.

Constraints

• 1\leq N\leq 2\times 10^5
• S is a string of length N consisting of 0 and 1.
• 1\leq W_i\leq 10^9
• N and W_i are integers.

Sample Input 1

5
10101
60 45 30 40 80

Sample Output 1

4

When Takahashi is given X=50, it judges the 2-nd, 3-rd, and 4-th people to be children and the 1-st and 5-th to be adults.
In reality, the 2-nd and 4-th are children, and the 1-st, 3-rd, and 5-th are adults, so the 1-st, 2-nd, 4-th, and 5-th people are correctly judged. Thus, f(50)=4.

This is the maximum since there is no X that judges correctly for all 5 people. Thus, 4 should be printed.

Sample Input 2

3
000
1 2 3

Sample Output 2

3

For example, X=10 achieves the maximum value f(10)=3.
Note that the people may be all children or all adults.

Sample Input 3

5
10101
60 50 50 50 60

Sample Output 3

4

For example, X=55 achieves the maximum value f(55)=4.
Note that there may be multiple people with the same weight.

Problem Statement

You are given a sequence of length N: A=(A_1,A_2,\dots,A_N). The following action on this sequence is called an operation.

• First, choose an integer i such that 1 \le i \le N.
• Next, choose and do one of the following.
  • Add 1 to A_i.
  • Subtract 1 from A_i.

Answer Q questions.
The i-th question is the following.

• Consider performing zero or more operations to change every element of A to X_i. Find the minimum number of operations required to do so.

Constraints

• All values in input are integers.
• 1 \le N,Q \le 2 \times 10^5
• 0 \le A_i \le 10^9
• 0 \le X_i \le 10^9

Sample Input 1

5 3
6 11 2 5 5
5
20
0

Sample Output 1

10
71
29

We have A=(6,11,2,5,5) and three questions in this input.

For the 1-st question, you can change every element of A to 5 in 10 operations as follows.

• Subtract 1 from A_1.
• Subtract 1 from A_2 six times.
• Add 1 to A_3 three times.

It is impossible to change every element of A to 5 in 9 or fewer operations.

For the 2-nd question, you can change every element of A to 20 in 71 operations.

For the 3-rd question, you can change every element of A to 0 in 29 operations.

Sample Input 2

10 5
1000000000 314159265 271828182 141421356 161803398 0 777777777 255255255 536870912 998244353
555555555
321654987
1000000000
789456123
0

Sample Output 2

3316905982
2811735560
5542639502
4275864946
4457360498

The output may not fit into 32-bit integers.