Problem Statement

Team Takahashi and Team Aoki played N matches. In the i-th match (1\leq i\leq N), Team Takahashi scored X _ i points, and Team Aoki scored Y _ i points.

The team with the higher total score from the N matches wins.

Print the winner. If the two teams have the same total score, it is a draw.

Constraints

• 1\leq N\leq 100
• 0\leq X _ i\leq 100\ (1\leq i\leq N)
• 0\leq Y _ i\leq 100\ (1\leq i\leq N)
• All input values are integers.

Sample Input 1

4
10 2
10 1
10 2
3 2

Sample Output 1

Takahashi

In four matches, Team Takahashi scored 33 points, and Team Aoki scored 7 points. Team Takahashi wins, so print Takahashi.

Sample Input 2

6
5 4
4 5
2 4
1 6
7 1
3 2

Sample Output 2

Draw

Both teams scored 22 points. It is a draw, so print Draw.

Sample Input 3

4
0 0
10 10
50 50
0 100

Sample Output 3

Aoki

One or both teams may score no points in a match.

Problem Statement

In the hexadecimal system, where the digits ABCDEF corresponding to 10,11,12,13,14, and 15 are used in addition to 0123456789, every integer between 0 and 255 is represented as a 1- or 2-digit numeral.
For example, 0 and 12 are represented as 1-digit hexadecimal numerals 0 and C; 99 and 255 are represented as 2-digit hexadecimals 63 and FF.

Given an integer N between 0 and 255, convert it to an exactly two-digit hexadecimal numeral, prepending leading 0s if necessary.

Notes

The judge is case-sensitive. Specifically, you cannot use abcdef as hexadecimal digits instead of ABCDEF.

Constraints

• 0 \leq N \leq 255
• N is an integer.

Sample Input 1

99

Sample Output 1

63

99 is represented as 63 in hexadecimal.

Sample Input 2

12

Sample Output 2

0C

12 is represented as C in hexadecimal.
Since we ask you to convert it to a two-digit hexadecimal numeral, the answer is 0C, where 0 is prepended to C.

Sample Input 3

0

Sample Output 3

00

Sample Input 4

255

Sample Output 4

FF

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 is a simple undirected graph G with N vertices labeled with numbers 1, 2, \ldots, N.

You are given the adjacency matrix (A_{i,j}) of G. That is, G has an edge connecting vertices i and j if and only if A_{i,j} = 1.

For each i = 1, 2, \ldots, N, print the numbers of the vertices directly connected to vertex i in ascending order.

Here, vertices i and j are said to be directly connected if and only if there is an edge connecting vertices i and j.

Constraints

• 2 \leq N \leq 100
• A_{i,j} \in \lbrace 0,1 \rbrace
• A_{i,i} = 0
• A_{i,j} = A_{j,i}
• All input values are integers.

Sample Input 1

4
0 1 1 0
1 0 0 1
1 0 0 0
0 1 0 0

Sample Output 1

2 3
1 4
1
2

Vertex 1 is directly connected to vertices 2 and 3. Thus, the first line should contain 2 and 3 in this order.

Similarly, the second line should contain 1 and 4 in this order, the third line should contain 1, and the fourth line should contain 2.

Sample Input 2

2
0 0
0 0

Sample Output 2

G may have no edges.

Sample Input 3

5
0 1 0 1 1
1 0 0 1 0
0 0 0 0 1
1 1 0 0 1
1 0 1 1 0

Sample Output 3

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

Problem Statement

Takahashi sent a string T consisting of lowercase English letters to Aoki. As a result, Aoki received a string T' consisting of lowercase English letters.

T' may have been altered from T. Specifically, exactly one of the following four conditions is known to hold.

• T' is equal to T.
• T' is a string obtained by inserting one lowercase English letter at one position (possibly the beginning and end) in T.
• T' is a string obtained by deleting one character from T.
• T' is a string obtained by changing one character in T to another lowercase English letter.

You are given the string T' received by Aoki and N strings S_1, S_2, \ldots, S_N consisting of lowercase English letters. Find all the strings among S_1, S_2, \ldots, S_N that could equal the string T sent by Takahashi.

Constraints

• N is an integer.
• 1 \leq N \leq 5 \times 10^5
• S_i and T' are strings of length between 1 and 5 \times 10^5, inclusive, consisting of lowercase English letters.
• The total length of S_1, S_2, \ldots, S_N is at most 5 \times 10^5.

Sample Input 1

5 ababc
ababc
babc
abacbc
abdbc
abbac

Sample Output 1

4
1 2 3 4

Among S_1, S_2, \ldots, S_5, the strings that could be equal to T are S_1, S_2, S_3, S_4, as explained below.

• S_1 could be equal to T, because T' = ababc is equal to S_1 = ababc.
• S_2 could be equal to T, because T' = ababc is obtained by inserting the letter a at the beginning of S_2 = babc.
• S_3 could be equal to T, because T' = ababc is obtained by deleting the fourth character c from S_3 = abacbc.
• S_4 could be equal to T, because T' = ababc is obtained by changing the third character d in S_4 = abdbc to b.
• S_5 could not be equal to T, because if we take S_5 = abbac as T, then T' = ababc does not satisfy any of the four conditions in the problem statement.

Sample Input 2

1 aoki
takahashi

Sample Output 2

0

Sample Input 3

9 atcoder
atoder
atcode
athqcoder
atcoder
tacoder
jttcoder
atoder
atceoder
atcoer

Sample Output 3

6
1 2 4 7 8 9