Problem Statement

There are N cities numbered 1, \dots, N, and M roads connecting cities.
The i-th road (1 \leq i \leq M) connects city A_i and city B_i.

Print N lines as follows.

• Let d_i be the number of cities directly connected to city i \, (1 \leq i \leq N), and those cities be city a_{i, 1}, \dots, city a_{i, d_i}, in ascending order.
• The i-th line (1 \leq i \leq N) should contain d_i + 1 integers d_i, a_{i, 1}, \dots, a_{i, d_i} in this order, separated by spaces.

Constraints

• 2 \leq N \leq 10^5
• 1 \leq M \leq 10^5
• 1 \leq A_i \lt B_i \leq N \, (1 \leq i \leq M)
• (A_i, B_i) \neq (A_j, B_j) if (i \neq j).
• All values in the input are integers.

Sample Input 1

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

Sample Output 1

3 2 3 6
2 1 5
2 1 6
0
2 2 6
3 1 3 5

The cities directly connected to city 1 are city 2, city 3, and city 6. Thus, we have d_1 = 3, a_{1, 1} = 2, a_{1, 2} = 3, a_{1, 3} = 6, so you should print 3, 2, 3, 6 in the first line in this order, separated by spaces.

Note that a_{i, 1}, \dots, a_{i, d_i} must be in ascending order. For instance, it is unacceptable to print 3, 3, 2, 6 in the first line in this order.

Sample Input 2

5 10
1 2
1 3
1 4
1 5
2 3
2 4
2 5
3 4
3 5
4 5

Sample Output 2

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

Problem Statement

You are given a positive integer N. Print a string of length (N+1), s_0s_1\ldots s_N, defined as follows.

For each i = 0, 1, 2, \ldots, N,

• if there is a divisor j of N that is between 1 and 9, inclusive, and i is a multiple of N/j, then s_i is the digit corresponding to the smallest such j (s_i will thus be one of 1, 2, ..., 9);
• if no such j exists, then s_i is -.

Constraints

• 1 \leq N \leq 1000
• All input values are integers.

Sample Input 1

12

Sample Output 1

1-643-2-346-1

We will explain how to determine s_i for some i.

• For i = 0, the divisors j of N between 1 and 9 such that i is a multiple of N/j are 1, 2, 3, 4, 6. The smallest of these is 1, so s_0 = 1.

• For i = 4, the divisors j of N between 1 and 9 such that i is a multiple of N/j are 3, 6. The smallest of these is 3, so s_4 = 3.

• For i = 11, there are no divisors j of N between 1 and 9 such that i is a multiple of N/j, so s_{11} = -.

Sample Input 2

7

Sample Output 2

17777771

Sample Input 3

1

Sample Output 3

11

Problem Statement

There are N people in an xy-plane. Person i is at (X_i, Y_i). The positions of all people are different.

We have a string S of length N consisting of L and R.
If S_i = R, Person i is facing right; if S_i = L, Person i is facing left. All people simultaneously start walking in the direction they are facing. Here, right and left correspond to the positive and negative x-direction, respectively.

For example, the figure below shows the movement of people when (X_1, Y_1) = (2, 3), (X_2, Y_2) = (1, 1), (X_3, Y_3) =(4, 1), S = RRL.

We say that there is a collision when two people walking in opposite directions come to the same position. Will there be a collision if all people continue walking indefinitely?

Constraints

• 2 \leq N \leq 2 \times 10^5
• 0 \leq X_i \leq 10^9
• 0 \leq Y_i \leq 10^9
• (X_i, Y_i) \neq (X_j, Y_j) if i \neq j.
• All X_i and Y_i are integers.
• S is a string of length N consisting of L and R.

Sample Input 1

3
2 3
1 1
4 1
RRL

Sample Output 1

Yes

This input corresponds to the example in the Problem Statement.
If all people continue walking, Person 2 and Person 3 will collide. Thus, Yes should be printed.

Sample Input 2

2
1 1
2 1
RR

Sample Output 2

No

Since Person 1 and Person 2 walk in the same direction, they never collide.

Sample Input 3

10
1 3
1 4
0 0
0 2
0 4
3 1
2 4
4 2
4 4
3 3
RLRRRLRLRR

Sample Output 3

Yes

Problem Statement

You are given positive integers N and Q, and a string S of length N consisting of lowercase English letters.

Process Q queries. Each query is of one of the following two types.

• 1 x: Perform the following x times in a row: delete the last character of S and append it to the beginning.
• 2 x: Print the x-th character of S.

Constraints

• 2 \le N \le 5 \times 10^5
• 1 \le Q \le 5 \times 10^5
• 1 \le x \le N
• |S|=N
• S consists of lowercase English letters.
• At least one query in the format 2 x.
• N, Q, x are all integers.

Sample Input 1

3 3
abc
2 2
1 1
2 2

Sample Output 1

b
a

In the 1-st query, S is abc, so the 2-nd character b should be printed. In the 2-nd query, S is changed from abc to cab. In the 3-rd query, S is cab, so the 2-nd character a should be printed.

Sample Input 2

10 8
dsuccxulnl
2 4
2 7
1 2
2 7
1 1
1 2
1 3
2 5

Sample Output 2

c
u
c
u

Problem Statement

A polyomino is a puzzle piece in the shape of a connected polygon made by connecting several squares by their edges.

There is a grid with four rows and four columns, and three polyominoes that fit within the grid.
The shape of the i-th polyomino is represented by 16 characters P_{i,j,k} (1 \leq j, k \leq 4). They describe the state of the grid when the i-th polyomino is placed on it. If P_{i, j, k} is #, the square at the j-th row from the top and k-th column from the left is occupied by the polyomino; if it is ., the square is not occupied. (Refer to the figures at Sample Input/Output 1.)

You want to fill the grid with all three polyominoes so that all of the following conditions are satisfied.

• All squares of the grid are covered by the polyominoes.
• The polyominoes must not overlap each other.
• The polyominoes must not stick out of the grid.
• The polyominoes may be freely translated and rotated but may not be flipped over.

Can the grid be filled with the polyominoes to satisfy these conditions?

Constraints

• P_{i, j, k} is # or ..
• The given polyominoes are connected. In other words, the squares that make up a polyomino can be reached from each other by following only the squares up, down, left, and right.
• The given polyominoes are not empty.

Sample Input 1

....
###.
.#..
....
....
.###
.##.
....
..#.
.##.
.##.
.##.

Sample Output 1

Yes

The figure below shows the shapes of the polyominoes corresponding to Sample Input 1.

In this case, you can fill the grid with them to satisfy the conditions in the problem statement by placing them as shown in the figure below.

Thus, the answer is Yes.

Sample Input 2

###.
#.#.
##..
....
....
..#.
....
....
####
##..
#...
#...

Sample Output 2

Yes

As in the first polyomino in Sample Input 2, a polyomino may be in the shape of a polygon with a hole.

Sample Input 3

##..
#..#
####
....
....
##..
.##.
....
.#..
.#..
.#..
.#..

Sample Output 3

No

Note that the polyominoes may not be flipped over when filling the grid.

Sample Input 4

....
..#.
....
....
....
..#.
....
....
....
..#.
....
....

Sample Output 4

No

Sample Input 5

....
####
#...
#...
....
####
...#
..##
....
..##
..#.
..##

Sample Output 5

No

Sample Input 6

###.
.##.
..#.
.###
....
...#
..##
...#
....
#...
#...
#...

Sample Output 6

Yes