Problem Statement

You are given a string s consisting of two kinds of characters, 0 and 1. Print the string obtained by replacing 0 with 1 and 1 with 0 in s.

Constraints

• The length of s is between 1 and 10, inclusive.
• s consists of two kinds of characters, 0 and 1.

Sample Input 1

01

Sample Output 1

10

The 1-st character of s is 1, so the 1-st character to print is 0. The 2-nd character of s is 0, so the 2-nd character to print is 1.

Sample Input 2

1011

Sample Output 2

0100

Sample Input 3

100100001

Sample Output 3

011011110

Problem Statement

There is a stack of N cards, and the i-th card from the top has an integer A_i written on it.

You take K cards from the bottom of the stack and place them on top of the stack, maintaining their order.

Print the integers written on the cards from top to bottom after the operation.

Constraints

• 1 \leq K < N \leq 100
• 1 \leq A_i \leq 100
• All input values are integers.

Sample Input 1

5 3
1 2 3 4 5

Sample Output 1

3 4 5 1 2

Initially, the integers written on the cards are 1,2,3,4,5 from top to bottom.

After taking three cards from the bottom of the stack and placing them on top, the integers written on the cards become 3,4,5,1,2 from top to bottom.

Sample Input 2

6 2
1 2 1 2 1 2

Sample Output 2

1 2 1 2 1 2

The integers written on the cards are not necessarily distinct.

Problem Statement

We have a sequence of length N consisting of positive integers: A=(A_1,\ldots,A_N). Any two adjacent terms have different values.

Let us insert some numbers into this sequence by the following procedure.

1. If every pair of adjacent terms in A has an absolute difference of 1, terminate the procedure.
2. Let A_i, A_{i+1} be the pair of adjacent terms nearest to the beginning of A whose absolute difference is not 1.
   • If A_i < A_{i+1}, insert A_i+1,A_i+2,\ldots,A_{i+1}-1 between A_i and A_{i+1}.
   • If A_i > A_{i+1}, insert A_i-1,A_i-2,\ldots,A_{i+1}+1 between A_i and A_{i+1}.
3. Return to step 1.

Print the sequence when the procedure ends.

Constraints

• 2 \leq N \leq 100
• 1 \leq A_i \leq 100
• A_i \neq A_{i+1}
• All values in the input are integers.

Sample Input 1

4
2 5 1 2

Sample Output 1

2 3 4 5 4 3 2 1 2

The initial sequence is (2,5,1,2). The procedure goes as follows.

• Insert 3,4 between the first term 2 and the second term 5, making the sequence (2,3,4,5,1,2).
• Insert 4,3,2 between the fourth term 5 and the fifth term 1, making the sequence (2,3,4,5,4,3,2,1,2).

Sample Input 2

6
3 4 5 6 5 4

Sample Output 2

3 4 5 6 5 4

No insertions may be performed.

Problem Statement

There are N rectangular sheets spread out on a coordinate plane.

Each side of the rectangular region covered by each sheet is parallel to the x- or y-axis.
Specifically, the i-th sheet covers exactly the region satisfying A_i \leq x\leq B_i and C_i \leq y\leq D_i.

Let S be the area of the region covered by one or more sheets. It can be proved that S is an integer under the constraints.
Print S as an integer.

Constraints

• 2\leq N\leq 100
• 0\leq A_i<B_i\leq 100
• 0\leq C_i<D_i\leq 100
• All input values are integers.

Sample Input 1

3
0 5 1 3
1 4 0 5
2 5 2 4

Sample Output 1

20

The three sheets cover the following regions.
Here, red, yellow, and blue represent the regions covered by the first, second, and third sheets, respectively.

Therefore, the area of the region covered by one or more sheets is S=20.

Sample Input 2

2
0 100 0 100
0 100 0 100

Sample Output 2

10000

Note that different sheets may cover the same region.

Sample Input 3

3
0 1 0 1
0 3 0 5
5 10 0 10

Sample Output 3

65

Problem Statement

There is a slot machine with N reels.
The placement of symbols on the i-th reel is represented by a string S_i of length 10 containing each of 0, 1, \ldots, 9 exactly once.

Each reel has a corresponding button. For each non-negative integer t, Takahashi can press one of the buttons of his choice (or do nothing) t seconds after the reels start spinning.
If the button for the i-th reel is pressed t seconds after the start of the spin, the i-th reel will stop to display the ((t\bmod{10})+1)-th character of S_i.
Here, t\bmod{10} denotes the remainder when t is divided by 10.

Takahashi wants to stop all reels to make them display the same character.
Find the minimum number of seconds needed to achieve his objective after the start of the spin.

Constraints

• 2\leq N\leq 100
• N is an integer.
• S_i is a string of length 10 containing each of 0, 1, \ldots, 9 exactly once.

Sample Input 1

3
1937458062
8124690357
2385760149

Sample Output 1

6

Takahashi can make all reels display 8 in 6 seconds after the start of the spin by stopping them as follows.

• 0 seconds after the start of the spin, press the button for the 2-nd reel, making it stop to display the ((0\bmod{10})+1=1)-st character of S_2, 8.
• 2 seconds after the start of the spin, press the button for the 3-rd reel, making it stop to display the ((2\bmod{10})+1=3)-rd character of S_3, 8.
• 6 seconds after the start of the spin, press the button for the 1-st reel, making it stop to display the ((6\bmod{10})+1=7)-th character of S_1, 8.

There is no way to make all reels display the same character in five seconds or less, so the answer is 6.

Sample Input 2

5
0123456789
0123456789
0123456789
0123456789
0123456789

Sample Output 2

40

Note that he must stop all reels to make them display the same character.

Problem Statement

There are zero or more sensors placed on a grid of H rows and W columns. Let (i, j) denote the square in the i-th row from the top and the j-th column from the left.
Whether each square contains a sensor is given by the strings S_1, S_2, \ldots, S_H, each of length W. (i, j) contains a sensor if and only if the j-th character of S_i is #.
These sensors interact with other sensors in the squares horizontally, vertically, or diagonally adjacent to them and operate as one sensor. Here, a cell (x, y) and a cell (x', y') are said to be horizontally, vertically, or diagonally adjacent if and only if \max(|x-x'|,|y-y'|) = 1.
Note that if sensor A interacts with sensor B and sensor A interacts with sensor C, then sensor B and sensor C also interact.

Considering the interacting sensors as one sensor, find the number of sensors on this grid.

Constraints

• 1 \leq H, W \leq 1000
• H and W are integers.
• S_i is a string of length W where each character is # or ..

Sample Input 1

5 6
.##...
...#..
....##
#.#...
..#...

Sample Output 1

3

When considering the interacting sensors as one sensor, the following three sensors exist:

• The interacting sensors at (1,2),(1,3),(2,4),(3,5),(3,6)
• The sensor at (4,1)
• The interacting sensors at (4,3),(5,3)

Sample Input 2

3 3
#.#
.#.
#.#

Sample Output 2

1

Sample Input 3

4 2
..
..
..
..

Sample Output 3

0

Sample Input 4

5 47
.#..#..#####..#...#..#####..#...#...###...#####
.#.#...#.......#.#...#......##..#..#...#..#....
.##....#####....#....#####..#.#.#..#......#####
.#.#...#........#....#......#..##..#...#..#....
.#..#..#####....#....#####..#...#...###...#####

Sample Output 4

7

Problem Statement

There is a H \times W-square grid with H horizontal rows and W vertical columns. Let (i, j) denote the square at the i-th row from the top and j-th column from the left.
Each square is described by a character C_{i, j}, where C_{i, j} = . means (i, j) is an empty square, and C_{i, j} = # means (i, j) is a wall.

Takahashi is about to start walking in this grid. When he is on (i, j), he can go to (i, j + 1) or (i + 1, j). However, he cannot exit the grid or enter a wall square. He will stop when there is no more square to go to.

When starting on (1, 1), at most how many squares can Takahashi visit before he stops?

Constraints

• 1 \leq H, W \leq 100
• H and W are integers.
• C_{i, j} = . or C_{i, j} = #. (1 \leq i \leq H, 1 \leq j \leq W)
• C_{1, 1} = .

Sample Input 1

3 4
.#..
..#.
..##

Sample Output 1

4

For example, by going (1, 1) \rightarrow (2, 1) \rightarrow (2, 2) \rightarrow (3, 2), he can visit 4 squares.

He cannot visit 5 or more squares, so we should print 4.

Sample Input 2

1 1
.

Sample Output 2

1

Sample Input 3

5 5
.....
.....
.....
.....
.....

Sample Output 3

9

Problem Statement

You are given a positive integer N and a sequence of positive integers C=(C_1,C_2,\ldots,C_N) of length N.

Find, modulo a given positive integer M, the number of sequences of positive integers that satisfy all of the following conditions.

• All elements of the sequence are between 1 and N, inclusive.
• For each i=1,2,\ldots,N, the value i appears exactly C_i times in the sequence.

T test cases are given, so find the answer for each. M is common to all T test cases.

Constraints

• 1\leq T\leq 10^5
• 2\leq M\leq 10^9
• 1\leq N
• 1\leq C_i
• \sum_{i=1}^N C_i\leq 5000
• The sum of N over all test cases is at most 3\times 10^5.
• All input values are integers.

Sample Input 1

3 1000000000
2
2 2
5
1 1 1 1 1
6
1 2 3 4 5 6

Sample Output 1

6
120
230379200

For the first test case, the sequences that satisfy the conditions are (1,1,2,2),(1,2,1,2),(1,2,2,1),(2,1,1,2),(2,1,2,1),(2,2,1,1), which is six sequences.

Sample Input 2

3 998244353
1
1
3
4 2 5
10
500 500 500 500 500 500 500 500 500 500

Sample Output 2

1
6930
261233246

Problem Statement

Takahashi and a cargo are on a coordinate plane.

Takahashi is currently at (X_A,Y_A), and the cargo is at (X_B,Y_B). He wants to move the cargo to (X_C,Y_C).

When he is at (x,y), he can make one of the following moves in a single action.

• Move to (x+1,y). If the cargo is at (x+1,y) before the move, move it to (x+2,y).
• Move to (x-1,y). If the cargo is at (x-1,y) before the move, move it to (x-2,y).
• Move to (x,y+1). If the cargo is at (x,y+1) before the move, move it to (x,y+2).
• Move to (x,y-1). If the cargo is at (x,y-1) before the move, move it to (x,y-2).

Find the minimum number of actions required to move the cargo to (X_C,Y_C).

Constraints

• -10^{17}\leq X_A,Y_A,X_B,Y_B,X_C,Y_C\leq 10^{17}
• (X_A,Y_A)\neq (X_B,Y_B)
• (X_B,Y_B)\neq (X_C,Y_C)
• All input values are integers.

Sample Input 1

1 2 3 3 0 5

Sample Output 1

9

Takahashi can move the cargo to (0,5) in nine actions as follows.

• Move to (2,2).
• Move to (3,2).
• Move to (3,3). The cargo moves to (3,4).
• Move to (3,4). The cargo moves to (3,5).
• Move to (4,4).
• Move to (4,5).
• Move to (3,5). The cargo moves to (2,5).
• Move to (2,5). The cargo moves to (1,5).
• Move to (1,5). The cargo moves to (0,5).

It is impossible to move the cargo to (0,5) in eight or fewer actions, so you should print 9.

Sample Input 2

0 0 1 0 -1 0

Sample Output 2

6

Sample Input 3

-100000000000000000 -100000000000000000 100000000000000000 100000000000000000 -100000000000000000 -100000000000000000

Sample Output 3

800000000000000003