Problem Statement

We have a grid with H horizontal rows and W vertical columns. (i, j) denotes the square at the i-th row from the top and j-th column from the left.
(i,j) has a character G_{i,j} written on it. G_{i,j} is U, D, L, or R.

You are initially at (1,1). You repeat the following operation until you cannot make a move.

Let (i,j) be the square you are currently at.
If G_{i,j} is U and i \neq 1, move to (i-1,j).
If G_{i,j} is D and i \neq H, move to (i+1,j).
If G_{i,j} is L and j \neq 1, move to (i,j-1).
If G_{i,j} is R and j \neq W, move to (i,j+1).
Otherwise, you cannot make a move.

Print the square you end up at when you cannot make a move.
If you indefinitely repeat moving, print -1 instead.

Constraints

• 1 \leq H, W \leq 500
• G_{i,j} is U, D, L, or R.
• H and W are integers.

Sample Input 1

2 3
RDU
LRU

Sample Output 1

1 3

You will move as (1, 1) \to (1, 2) \to (2, 2) \to (2, 3) \to (1, 3), ending up here, so the answer is (1, 3).

Sample Input 2

2 3
RRD
ULL

Sample Output 2

-1

You will indefinitely repeat moving as (1, 1) \to (1, 2) \to (1, 3) \to (2, 3) \to (2, 2) \to (2, 1) \to (1, 1) \to (1, 2) \to \dots, so -1 should be printed in this case.

Sample Input 3

9 44
RRDDDDRRRDDDRRRRRRDDDRDDDDRDDRDDDDDDRRDRRRRR
RRRDLRDRDLLLLRDRRLLLDDRDLLLRDDDLLLDRRLLLLLDD
DRDLRLDRDLRDRLDRLRDDLDDLRDRLDRLDDRLRRLRRRDRR
DDLRRDLDDLDDRLDDLDRDDRDDDDRLRRLRDDRRRLDRDRDD
RDLRRDLRDLLLLRRDLRDRRDRRRDLRDDLLLLDDDLLLLRDR
RDLLLLLRDLRDRLDDLDDRDRRDRLDRRRLDDDLDDDRDDLDR
RDLRRDLDDLRDRLRDLDDDLDDRLDRDRDLDRDLDDLRRDLRR
RDLDRRLDRLLLLDRDRLLLRDDLLLLLRDRLLLRRRRLLLDDR
RRRRDRDDRRRDDRDDDRRRDRDRDRDRRRRRRDDDRDDDDRRR

Sample Output 3

9 5

Problem Statement

There is a directed graph with N vertices and N edges.
The i-th edge goes from vertex i to vertex A_i. (The constraints guarantee that i \neq A_i.)
Find a directed cycle without the same vertex appearing multiple times.
It can be shown that a solution exists under the constraints of this problem.

Notes

The sequence of vertices B = (B_1, B_2, \dots, B_M) is called a directed cycle when all of the following conditions are satisfied:

• M \geq 2
• The edge from vertex B_i to vertex B_{i+1} exists. (1 \leq i \leq M-1)
• The edge from vertex B_M to vertex B_1 exists.
• If i \neq j, then B_i \neq B_j.

Constraints

• All input values are integers.
• 2 \le N \le 2 \times 10^5
• 1 \le A_i \le N
• A_i \neq i

Sample Input 1

7
6 7 2 1 3 4 5

Sample Output 1

4
7 5 3 2

7 \rightarrow 5 \rightarrow 3 \rightarrow 2 \rightarrow 7 is indeed a directed cycle.

Here is the graph corresponding to this input:

Here are other acceptable outputs:

4
2 7 5 3

3
4 1 6

Note that the graph may not be connected.

Sample Input 2

2
2 1

Sample Output 2

2
1 2

This case contains both of the edges 1 \rightarrow 2 and 2 \rightarrow 1.
In this case, 1 \rightarrow 2 \rightarrow 1 is indeed a directed cycle.

Here is the graph corresponding to this input, where 1 \leftrightarrow 2 represents the existence of both 1 \rightarrow 2 and 2 \rightarrow 1:

Sample Input 3

8
3 7 4 7 3 3 8 2

Sample Output 3

3
2 7 8

Here is the graph corresponding to this input:

Problem Statement

The Republic of AtCoder lies on a Cartesian coordinate plane.
It has N towns, numbered 1,2,\dots,N. Town i is at (x_i, y_i), and no two different towns are at the same coordinates.

There are teleportation spells in the nation. A spell is identified by a pair of integers (a,b), and casting a spell (a, b) at coordinates (x, y) teleports you to (x+a, y+b).

Snuke is a great magician who can learn the spell (a, b) for any pair of integers (a, b) of his choice. The number of spells he can learn is also unlimited.
To be able to travel between the towns using spells, he has decided to learn some number of spells so that it is possible to do the following for every pair of different towns (i, j).

• Choose just one spell among the spells learned. Then, repeatedly use just the chosen spell to get from Town i to Town j.

At least how many spells does Snuke need to learn to achieve the objective above?

Constraints

• 2 \leq N \leq 500
• 0 \leq x_i \leq 10^9 (1 \leq i \leq N)
• 0 \leq y_i \leq 10^9 (1 \leq i \leq N)
• (x_i, y_i) \neq (x_j, y_j) if i \neq j.

Sample Input 1

3
1 2
3 6
7 4

Sample Output 1

6

The figure below illustrates the positions of the towns (along with the coordinates of the four corners).

If Snuke learns the six spells below, he can get from Town i to Town j by using one of the spells once for every pair (i,j) (i \neq j), achieving his objective.

• (2, 4)
• (-2, -4)
• (4, -2)
• (-4, 2)
• (-6, -2)
• (6, 2)

Another option is to learn the six spells below. In this case, he can get from Town i to Town j by using one of the spells twice for every pair (i,j) (i \neq j), achieving his objective.

• (1, 2)
• (-1, -2)
• (2, -1)
• (-2, 1)
• (-3, -1)
• (3, 1)

There is no combination of spells that consists of less than six spells and achieve the objective, so we should print 6.

Sample Input 2

3
1 2
2 2
4 2

Sample Output 2

2

The optimal choice is to learn the two spells below:

• (1, 0)
• (-1, 0)

Sample Input 3

4
0 0
0 1000000000
1000000000 0
1000000000 1000000000

Sample Output 3

8

Problem Statement

We have a simple undirected graph with N vertices and M edges. The vertices are numbered 1,\ldots,N. For each i=1,\ldots,M, the i-th edge connects Vertex a_i and Vertex b_i. Additionally, the degree of each vertex is at most 3.

For each i=1,\ldots,Q, answer the following query.

• Find the sum of indices of vertices whose distances from Vertex x_i are at most k_i.

Constraints

• 1 \leq N \leq 1.5 \times 10^5
• 0 \leq M \leq \min (\frac{N(N-1)}{2},\frac{3N}{2})
• 1 \leq a_i \lt b_i \leq N
• (a_i,b_i) \neq (a_j,b_j), if i\neq j.
• The degree of each vertex in the graph is at most 3.
• 1 \leq Q \leq 1.5 \times 10^5
• 1 \leq x_i \leq N
• 0 \leq k_i \leq 3
• All values in input are integers.

Sample Input 1

6 5
2 3
3 4
3 5
5 6
2 6
7
1 1
2 2
2 0
2 3
4 1
6 0
4 3

Sample Output 1

1
20
2
20
7
6
20

For the 1-st query, the only vertex whose distance from Vertex 1 is at most 1 is Vertex 1, so the answer is 1.
For the 2-nd query, the vertices whose distances from Vertex 2 are at most 2 are Vertex 2, 3, 4, 5, and 6, so the answer is their sum, 20.
The 3-rd and subsequent queries can be answered similarly.

Problem Statement

There is a grid with H rows and W columns. Initially, each integer from 1 to (H \times W) is written exactly once in the grid.
Specifically, for 1 \leq i \leq H and 1 \leq j \leq W, the cell at the i-th row from the top and the j-th column from the left contains S_{i,j}.
Below, let (i,j) denote the cell at the i-th row from the top and the j-th column from the left.

Determine if it is possible to reach a state where, for all pairs of integers (i,j) (1 \leq i \leq H, 1 \leq j \leq W),
the cell (i,j) contains the integer ((i-1) \times W + j) by repeating the following operation at most 20 times (possibly zero).
If it is possible, print the minimum number of operations required.
If it is impossible in 20 or fewer operations (including the case where it is impossible no matter how many times the operation is repeated), print -1.

Operation: Choose a rectangle of size (H-1) \times (W-1) from the grid and rotate it 180 degrees.
More precisely, choose integers x and y (0 \leq x, y \leq 1),
and for all pairs of integers (i,j) satisfying 1 \leq i \leq H-1 and 1 \leq j \leq W-1,
simultaneously replace the integer written in cell (i+x,j+y) with the number written in cell (H-i+x,W-j+y).

Note that it is only necessary for the integers written in the cells to satisfy the condition; the orientation in which they are written does not matter.

Constraints

• 3 \leq H,W \leq 8
• 1 \leq S_{i,j} \leq H \times W
• If (i,j) \neq (i',j'), then S_{i,j} \neq S_{i',j'}
• All input values are integers.

Sample Input 1

3 3
9 4 3
2 1 8
7 6 5

Sample Output 1

2

Operating in the following order will satisfy the conditions of the problem statement in 2 operations.

• Operate by choosing the rectangle in the top-left corner. That is, by choosing x=0 and y=0.
• Operate by choosing the rectangle in the bottom-right corner. That is, by choosing x=1 and y=1.

On the other hand, it is impossible to satisfy the conditions with one or fewer operations, so print 2.

Sample Input 2

4 6
15 18 1 14 3 4
23 24 19 8 9 12
13 2 17 6 5 16
21 22 7 20 11 10

Sample Output 2

-1

It is impossible to satisfy the conditions with 20 or fewer operations, so print -1.

Sample Input 3

4 6
1 4 13 16 15 18
21 20 9 12 23 10
17 14 5 6 3 2
11 22 7 24 19 8

Sample Output 3

20

Sample Input 4

4 3
1 2 3
4 5 6
7 8 9
10 11 12

Sample Output 4

0