Problem Statement

You are given a string S consisting of lowercase English letters. How many different non-empty substrings does S have?

A substring is a contiguous subsequence. For example, xxx is a substring of yxxxy but not of xxyxx.

Constraints

• S is a string of length between 1 and 100, inclusive, consisting of lowercase English letters.

Sample Input 1

yay

Sample Output 1

5

S has the following five different non-empty substrings:

• a
• y
• ay
• ya
• yay

Sample Input 2

aababc

Sample Output 2

17

Sample Input 3

abracadabra

Sample Output 3

54

Problem Statement

People 1,2,\dots,N (where N is odd) conducted M votes where each person chooses either 0 or 1.
Each person's vote for each round is given as N strings S_1,S_2,\dots,S_N of length M consisting of 0 and 1, where the j-th character of S_i represents person i's vote content for the j-th vote.

In each vote, people who were in the minority receive 1 point.
More precisely, points are given according to the following rules:

• Suppose x people chose 0 and y people chose 1 in that vote.
  • If x=0 or y=0, everyone receives 1 point for that vote.
  • Otherwise, if x<y, only people who voted 0 in that vote receive 1 point.
  • Otherwise, only people who voted 1 in that vote receive 1 point.
  • Note that since N is odd, x=y never occurs.

After finishing M votes, find all people who have the highest total score from those votes.

Constraints

• N is an odd number satisfying 1 \le N \le 99.
• M is an integer satisfying 1 \le M \le 100.
• S_i is a string of length M consisting of 0 and 1.

Sample Input 1

3 5
11100
10101
01110

Sample Output 1

2 3

In this case, three people conducted five votes.

• In the 1st vote, person 1 voted 1, person 2 voted 1, person 3 voted 0. Thus, only person 3 receives 1 point.
• In the 2nd vote, person 1 voted 1, person 2 voted 0, person 3 voted 1. Thus, only person 2 receives 1 point.
• In the 3rd vote, person 1 voted 1, person 2 voted 1, person 3 voted 1. Thus, everyone receives 1 point.
• In the 4th vote, person 1 voted 0, person 2 voted 0, person 3 voted 1. Thus, only person 3 receives 1 point.
• In the 5th vote, person 1 voted 0, person 2 voted 1, person 3 voted 0. Thus, only person 2 receives 1 point.

As a result, person 1 received a total of 1 points, person 2 received a total of 3 points, and person 3 received a total of 3 points.
Therefore, persons 2 and 3 have the highest total score. Output these in ascending order of person number.

Sample Input 2

5 4
0000
0000
0000
0000
0000

Sample Output 2

1 2 3 4 5

Sample Input 3

7 8
11010011
01000000
01111100
10111000
10011110
10100101
10010110

Sample Output 3

1 2 3

Problem Statement

There are M sets, called S_1, S_2, \dots, S_M, consisting of integers between 1 and N.
S_i consists of C_i integers a_{i, 1}, a_{i, 2}, \dots, a_{i, C_i}.

There are (2^M-1) ways to choose one or more sets from the M sets.
How many of them satisfy the following condition?

• For all integers x such that 1 \leq x \leq N, there is at least one chosen set containing x.

Constraints

• 1 \leq N \leq 10
• 1 \leq M \leq 10
• 1 \leq C_i \leq N
• 1 \leq a_{i,1} \lt a_{i,2} \lt \dots \lt a_{i,C_i} \leq N
• All values in the input are integers.

Sample Input 1

3 3
2
1 2
2
1 3
1
2

Sample Output 1

3

The sets given in the input are S_1 = \lbrace 1, 2 \rbrace, S_2 = \lbrace 1, 3 \rbrace, S_3 = \lbrace 2 \rbrace.
The following three ways satisfy the conditions in the Problem Statement:

• choosing S_1, S_2;
• choosing S_1, S_2, S_3;
• choosing S_2, S_3.

Sample Input 2

4 2
2
1 2
2
1 3

Sample Output 2

0

There may be no way to choose sets that satisfies the conditions in the Problem Statement.

Sample Input 3

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

Sample Output 3

18

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

There is a grid with H rows and W columns. We call the cell at the i-th row from the top (1\leq i\leq H) and j-th column from the left (1\leq j\leq W) as cell (i,j).

Initially, cell (i,j) is colored black if S_{i,j} is # and white if it is ..

Perform the following operation 10^{100} times:

• Let T be the set of cells that are colored white and have exactly one adjacent cell colored black. Color each cell in T black. Here, two cells (i_1,j_1) and (i_2,j_2) are adjacent if and only if |i_1-i_2|+|j_1-j_2|=1.

Find the number of cells that are colored black after all operations are completed.

Constraints

• 2\leq H,W
• HW\leq 3\times 10^5
• H and W are integers.
• S_{i,j} is # or ..

Sample Input 1

9 9
.........
.........
.........
.........
....#....
.........
.........
.........
.........

Sample Output 1

57

The grid changes as follows through the operations. (The number above represents the operation count. The first ten operations are displayed.)

Eventually, 57 cells are colored black.

Sample Input 2

2 2
..
..

Sample Output 2

0

Sample Input 3

10 10
..........
....#.....
#.......#.
......#...
.......#..
.....#....
..........
..........
..#...#...
.......#..

Sample Output 3

64