Problem Statement

You are given a string S of length N consisting of A, B, and C.
Find the position where ABC first appears as a (contiguous) substring in S. In other words, find the smallest integer n that satisfies all of the following conditions.

• 1 \leq n \leq N - 2.
• The string obtained by extracting the n-th through (n+2)-th characters of S is ABC.

If ABC does not appear in S, print -1.

Constraints

• 3 \leq N \leq 100
• S is a string of length N consisting of A, B, and C.

Sample Input 1

8
ABABCABC

Sample Output 1

3

ABC first appears in S at the 3-rd through 5-th characters of S. Therefore, the answer is 3.

Sample Input 2

3
ACB

Sample Output 2

-1

If ABC does not appear in S, print -1.

Sample Input 3

20
BBAAABBACAACABCBABAB

Sample Output 3

13

Problem Statement

There are four cards with integers A,B,C,D written on them.
Determine whether a Full House can be formed by adding one card.

A set of five cards is called a Full House if and only if the following condition is satisfied:

• For two distinct integers x and y, there are three cards with x written on them and two cards with y written on them.

Constraints

• All input values are integers.
• 1 \le A,B,C,D \le 13

Sample Input 1

7 7 7 1

Sample Output 1

Yes

Adding 1 to 7,7,7,1 forms a Full House.

Sample Input 2

13 12 11 10

Sample Output 2

No

Adding anything to 13,12,11,10 does not form a Full House.

Sample Input 3

3 3 5 5

Sample Output 3

Yes

Adding 3,3,5,5 to 3 forms a Full House.
Also, adding 5 forms a Full House.

Sample Input 4

8 8 8 8

Sample Output 4

No

Adding anything to 8,8,8,8 does not form a Full House.
Note that five identical cards do not form a Full House.

Sample Input 5

1 3 4 1

Sample Output 5

No

Problem Statement

You are given a positive integer N.

We have a grid with N rows and N columns, where the square at the i-th row from the top and j-th column from the left has a digit A_{i,j} written on it.

Assume that the upper and lower edges of this grid are connected, as well as the left and right edges. In other words, all of the following holds.

• (N,i) is just above (1,i), and (1,i) is just below (N,i). (1\le i\le N).
• (i,N) is just to the left of (i,1), and (i,1) is just to the right of (i,N). (1\le i\le N).

Takahashi will first choose one of the following eight directions: up, down, left, right, and the four diagonal directions. Then, he will start on a square of his choice and repeat moving one square in the chosen direction N-1 times.

In this process, Takahashi visits N squares. Find the greatest possible value of the integer that is obtained by arranging the digits written on the squares visited by Takahashi from left to right in the order visited by him.

Constraints

• 1 \le N \le 10
• 1 \le A_{i,j} \le 9
• All values in input are integers.

Sample Input 1

4
1161
1119
7111
1811

Sample Output 1

9786

If Takahashi starts on the square at the 2-nd row from the top and 4-th column from the left and goes down and to the right, the integer obtained by arranging the digits written on the visited squares will be 9786. It is impossible to make a value greater than 9786, so the answer is 9786.

Sample Input 2

10
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111
1111111111

Sample Output 2

1111111111

Note that the answer may not fit into a 32-bit integer.

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

The AtCoder Restaurant uses N types of ingredients numbered from 1 to N.

The restaurant offers M dishes numbered from 1 to M. Dish i uses K_i types of ingredients, namely A_{i,1}, A_{i,2}, \ldots, A_{i,K_i}.

Snuke currently dislikes all N ingredients. He cannot eat any dish that uses one or more ingredients he dislikes, and he can eat a dish that uses none of the disliked ingredients.

Over the next N days, he will overcome his dislikes one ingredient per day. On day i, he overcomes ingredient B_i, and from then on he no longer dislikes it.

For each i=1,2,\ldots,N, find:

• the number of dishes at the AtCoder Restaurant that he can eat immediately after overcoming ingredient B_i on day i.

Constraints

• 1 \leq N \leq 3 \times 10^{5}
• 1 \leq M \leq 3 \times 10^{5}
• 1 \leq K_i \leq N (1 \leq i \leq M)
• The sum of K_i is at most 3 \times 10^{5}.
• 1 \leq A_{i,j} \leq N (1 \leq i \leq M, 1 \leq j \leq K_i)
• A_{i,j} \neq A_{i,k} (1 \leq i \leq M, j \neq k)
• 1 \leq B_i \leq N (1 \leq i \leq N)
• B_i \neq B_j (i \neq j )
• All input values are integers.

Sample Input 1

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

Sample Output 1

0
1
2
3
4

Snuke overcomes his disliked ingredients as follows:

• Day 1: He overcomes ingredient 1. At this time, every dish still uses a disliked ingredient, so print 0.
• Day 2: He overcomes ingredient 3. Dish 4 no longer uses any disliked ingredient and becomes edible; all other dishes still use disliked ingredients, so print 1.
• Day 3: He overcomes ingredient 2. Dish 1 no longer uses any disliked ingredient and becomes edible; all dishes except 1 and 4 still use disliked ingredients, so print 2.
• Day 4: He overcomes ingredient 5. Dish 3 no longer uses any disliked ingredient and becomes edible; all dishes except 1, 3, and 4 still use disliked ingredients, so print 3.
• Day 5: He overcomes ingredient 4. Dish 2 no longer uses any disliked ingredient and becomes edible; now all dishes have no disliked ingredients, so print 4.

Sample Input 2

9 8
1 4
5 6 9 7 4 3
4 2 4 1 3
1 1
5 7 9 8 1 5
2 9 8
1 2
1 1
6 5 2 7 8 4 1 9 3

Sample Output 2

0
0
1
1
1
2
4
6
8