Problem Statement

Takahashi generated 10 strings S_1,S_2,\dots,S_{10} as follows.

• First, let S_i (1 \le i \le 10)= .......... (10 .s in a row).
• Next, choose four integers A, B, C, and D satisfying all of the following.
  • 1 \le A \le B \le 10.
  • 1 \le C \le D \le 10.
• Then, for every pair of integers (i,j) satisfying all of the following, replace the j-th character of S_i with #.
  • A \le i \le B.
  • C \le j \le D.

You are given S_1,S_2,\dots,S_{10} generated as above. Find the integers A, B, C, and D Takahashi chose.
It can be proved that such integers A, B, C, and D uniquely exist (there is just one answer) under the Constraints.

Constraints

• S_1,S_2,\dots,S_{10} are strings, each of length 10, that can be generated according to the Problem Statement.

Sample Input 1

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

Sample Output 1

5 8
4 9

Here, Takahashi chose A=5, B=8, C=4, D=9.
This choice generates 10 strings S_1,S_2,\dots,S_{10}, each of length 10, where the 4-th through 9-th characters of S_5,S_6,S_7,S_8 are #, and the other characters are ..
These are equal to the strings given in the input.

Sample Input 2

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

Sample Output 2

2 2
3 3

Sample Input 3

##########
##########
##########
##########
##########
##########
##########
##########
##########
##########

Sample Output 3

1 10
1 10

Problem Statement

There is a robot, and initially the weight of the robot is X. This robot has N types of parts that can be attached simultaneously: type 1, type 2,\ldots, type N. The weight of the type i\ (1\le i\le N) part is W _ i. Initially, none of the N types of parts are attached to the robot.

Process the following Q queries in order. The i-th query (1\le i\le Q) is represented by an integer P _ i and is as follows:

• If the type P _ i part is not currently attached to the robot, attach it; if it is attached, remove it. Then, print the current weight of the robot.

Constraints

• 1\le X\le100
• 1\le N\le100
• 1\le W _ i\le100\ (1\le i\le N)
• 1\le Q\le100
• 1\le P _ i\le N\ (1\le i\le Q)
• All input values are integers.

Sample Input 1

31
4
15 92 65 35
4
3
1
4
1

Sample Output 1

96
111
146
131

Initially, the weight of the robot is 31. For each query, the weight of the robot becomes as follows:

• In the 1-st query, attach the type 3 part to the robot. The weight of the robot becomes 31+65=96.
• In the 2-nd query, attach the type 1 part to the robot. The weight of the robot becomes 96+15=111.
• In the 3-rd query, attach the type 4 part to the robot. The weight of the robot becomes 111+35=146.
• In the 4-th query, remove the type 1 part from the robot. The weight of the robot becomes 146-15=131.

Sample Input 2

41
10
73 8 55 26 97 48 37 47 35 55
15
1
2
7
1
6
3
10
8
4
8
1
5
9
9
3

Sample Output 2

114
122
159
86
134
189
244
291
317
270
343
440
475
440
385

Problem Statement

There is a grid with N horizontal rows and N vertical columns, where each square is painted white or black.
The state of the grid is represented by N strings, S_i. If the j-th character of S_i is #, the square at the i-th row from the top and the j-th column from the left is painted black. If the character is ., then the square is painted white.

Takahashi can choose at most two of these squares that are painted white, and paint them black.
Determine if it is possible to make the grid contain 6 or more consecutive squares painted black aligned either vertically, horizontally, or diagonally.
Here, the grid is said to be containing 6 or more consecutive squares painted black aligned diagonally if the grid with N rows and N columns completely contains a subgrid with 6 rows and 6 columns such that all the squares on at least one of its diagonals are painted black.

Constraints

• 6 \leq N \leq 1000
• \lvert S_i\rvert =N
• S_i consists of # and ..

Sample Input 1

8
........
........
.#.##.#.
........
........
........
........
........

Sample Output 1

Yes

By painting the 3-rd and the 6-th squares from the left in the 3-rd row from the top, there will be 6 squares painted black aligned horizontally.

Sample Input 2

6
######
######
######
######
######
######

Sample Output 2

Yes

While Takahashi cannot choose a square to paint black, the grid already satisfies the condition.

Sample Input 3

10
..........
#..##.....
..........
..........
....#.....
....#.....
.#...#..#.
..........
..........
..........

Sample Output 3

No

Problem Statement

You are given a string S. Find the number of strings that can result from performing the following operation exactly once.

• Let N be the length of S. Choose a pair of integers (i,j) such that 1\leq i<j\leq N and swap the i-th and j-th characters of S.

It can be proved that you can always perform it under the constraints of this problem.

Constraints

• S is a string of length between 2 and 10^6, inclusive, consisting of lowercase English letters.

Sample Input 1

abc

Sample Output 1

3

The length of S is 3, so 1\leq i<j\leq 3 is satisfied by three pairs of integers (i,j): (1,2), (1,3), and (2,3).

• Swapping the 1-st and 2-nd characters of S results in S being bac.
• Swapping the 1-st and 3-rd characters of S results in S being cba.
• Swapping the 2-nd and 3-rd characters of S results in S being acb.

Therefore, the operation on abc results in one of the three strings: bac, cba, and acb, so print 3.

Sample Input 2

aaaaa

Sample Output 2

1

Swapping any two characters results in S remaining aaaaa. Thus, only one string can result from the operation.

Problem Statement

You are given N circles on the xy-coordinate plane. For each i = 1, 2, \ldots, N, the i-th circle is centered at (x_i, y_i) and has a radius of r_i.

Determine whether it is possible to get from (s_x, s_y) to (t_x, t_y) by only passing through points that lie on the circumference of at least one of the N circles.

Constraints

• 1 \leq N \leq 3000
• -10^9 \leq x_i, y_i \leq 10^9
• 1 \leq r_i \leq 10^9
• (s_x, s_y) lies on the circumference of at least one of the N circles.
• (t_x, t_y) lies on the circumference of at least one of the N circles.
• All values in input are integers.

Sample Input 1

4
0 -2 3 3
0 0 2
2 0 2
2 3 1
-3 3 3

Sample Output 1

Yes

Here is one way to get from (0, -2) to (3, 3).

• From (0, -2), pass through the circumference of the 1-st circle counterclockwise to reach (1, -\sqrt{3}).
• From (1, -\sqrt{3}), pass through the circumference of the 2-nd circle clockwise to reach (2, 2).
• From (2, 2), pass through the circumference of the 3-rd circle counterclockwise to reach (3, 3).

Thus, Yes should be printed.

Sample Input 2

3
0 1 0 3
0 0 1
0 0 2
0 0 3

Sample Output 2

No

It is impossible to get from (0, 1) to (0, 3) by only passing through points on the circumference of at least one of the circles, so No should be printed.