Problem Statement

You are given a 3-character string S, which is a concatenation of integers a and b between 1 and 9 (inclusive) and the character x in this order: axb.

Find the product of a and b.

Constraints

• The length of S is 3.
• The 1-st and 3-rd characters are digits between 1 and 9 (inclusive).
• The 2-nd character is x.

Sample Input 1

3x7

Sample Output 1

21

We have 3 \times 7 = 21, which should be printed.

Sample Input 2

9x9

Sample Output 2

81

Sample Input 3

1x1

Sample Output 3

1

Problem Statement

There are N boxes arranged in a row, and some of these boxes contain cookies.

The state of these boxes is represented by a string S of length N. Specifically, the i-th box (1\leq i \leq N) from the left contains one cookie if the i-th character of S is @, and is empty if it is ..

Over the next D days, Takahashi will choose and eat one cookie per day from among the cookies in these boxes.

Determine how many of the N boxes will be empty after D days have passed. (It can be proved that this value does not depend on which cookies Takahashi chooses each day.)

It is guaranteed that S contains at least D occurrences of @.

Constraints

• 1 \leq D \leq N \leq 100
• N and D are integers.
• S is a string of length N consisting of @ and ..
• S contains at least D occurrences of @.

Sample Input 1

5 2
.@@.@

Sample Output 1

4

For example, Takahashi might act as follows:

• Day 1: There are cookies in the 2nd, 3rd, and 5th boxes from the left. He chooses the cookie in the 2nd box to eat.
• Day 2: There are cookies in the 3rd and 5th boxes. He chooses the cookie in the 5th box to eat.
• After two days have passed, only the 3rd box from the left contains a cookie. Therefore, four out of the five boxes are empty.

Even though Takahashi might choose differently on each day than in this example, there will still be four empty boxes after two days. Therefore, the answer is 4.

Sample Input 2

3 3
@@@

Sample Output 2

3

Sample Input 3

10 4
@@@.@@.@@.

Sample Output 3

7

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

You are given a sequence A=(A_1,A_2,\dots,A_N) of length N and a sequence B=(B_1,B_2,\dots,B_M) of length M. Here, all elements of A and B are pairwise distinct. Determine whether the sequence C=(C_1,C_2,\dots,C_{N+M}) formed by sorting all elements of A and B in ascending order contains two consecutive elements appearing in A.

Constraints

• 1 \leq N, M \leq 100
• 1 \leq A_i, B_j \leq 200
• A_1, A_2, \dots, A_N, B_1, B_2, \dots, B_M are distinct.
• All input values are integers.

Sample Input 1

3 2
3 2 5
4 1

Sample Output 1

Yes

C=(1,2,3,4,5). Since 2 and 3 from A occur consecutively in C, print Yes.

Sample Input 2

3 2
3 1 5
4 2

Sample Output 2

No

C=(1,2,3,4,5). Since no two elements from A occur consecutively in C, print No.

Sample Input 3

1 1
1
2

Sample Output 3

No

Problem Statement

We have a playlist with N songs numbered 1, \dots, N.
Song i lasts A_i seconds.

When the playlist is played, song 1, song 2, \ldots, and song N play in this order. When song N ends, the playlist repeats itself, starting from song 1 again. While a song is playing, the next song does not play; when a song ends, the next song starts immediately.

At exactly T seconds after the playlist starts playing, which song is playing? Also, how many seconds have passed since the start of that song?
There is no input where the playlist changes songs at exactly T seconds after it starts playing.

Constraints

• 1 \leq N \leq 10^5
• 1 \leq T \leq 10^{18}
• 1 \leq A_i \leq 10^9
• The playlist does not change songs at exactly T seconds after it starts playing.
• All values in the input are integers.

Sample Input 1

3 600
180 240 120

Sample Output 1

1 60

When the playlist is played, the following happens. (Assume that it starts playing at time 0.)

• From time 0 to time 180, song 1 plays.
• From time 180 to time 420, song 2 plays.
• From time 420 to time 540, song 3 plays.
• From time 540 to time 720, song 1 plays.
• From time 720 to time 960, song 2 plays.
• \qquad\vdots

At time 600, song 1 is playing, and 60 seconds have passed since the start of that song.

Sample Input 2

3 281
94 94 94

Sample Output 2

3 93

Sample Input 3

10 5678912340
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000

Sample Output 3

6 678912340

Problem Statement

You are given an integer sequence A = (A_1, A_2, \ldots, A_N).

Find the minimum possible sum of all elements of A after performing the following operation exactly K times.

• Choose an integer x. For each i such that A_i = x, replace the value of A_i with 0.

Constraints

• 1 \leq K \leq N \leq 3 \times 10^5
• 1 \leq A_i \leq 10^9
• All input values are integers.

Sample Input 1

6 2
7 2 7 2 2 9

Sample Output 1

6

Initially, A = (7, 2, 7, 2, 2, 9).

Performing the operation with x = 9 gives A = (7, 2, 7, 2, 2, 0).

Next, performing the operation with x = 7 gives A = (0, 2, 0, 2, 2, 0).

At this point, the sum of all elements of A is 0 + 2 + 0 + 2 + 2 + 0 = 6.

Sample Input 2

8 6
1 2 3 4 1 2 3 4

Sample Output 2

0

Sample Input 3

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

Sample Output 3

8

Problem Statement

There is a grid with H rows and W columns. Let (i, j) denote the cell at the i-th row from the top and the j-th column from the left. The state of each cell is represented by the character A_{i,j}, which means the following:

• .: An empty cell.
• #: An obstacle.
• S: An empty cell and the start point.
• T: An empty cell and the goal point.

Takahashi can move from his current cell to a vertically or horizontally adjacent empty cell by consuming 1 energy. He cannot move if his energy is 0, nor can he exit the grid.

There are N medicines in the grid. The i-th medicine is at the empty cell (R_i, C_i) and can be used to set the energy to E_i. Note that the energy does not necessarily increase. He can use the medicine in his current cell. The used medicine will disappear.

Takahashi starts at the start point with 0 energy and wants to reach the goal point. Determine if this is possible.

Constraints

• 1 \leq H, W \leq 200
• A_{i, j} is one of ., #, S, and T.
• Each of S and T exists exactly once in A_{i, j}.
• 1 \leq N \leq 300
• 1 \leq R_i \leq H
• 1 \leq C_i \leq W
• (R_i, C_i) \neq (R_j, C_j) if i \neq j.
• A_{R_i, C_i} is not #.
• 1 \leq E_i \leq HW

Sample Input 1

4 4
S...
#..#
#...
..#T
4
1 1 3
1 3 5
3 2 1
2 3 1

Sample Output 1

Yes

For example, he can reach the goal point as follows:

• Use medicine 1. Energy becomes 3.
• Move to (1, 2). Energy becomes 2.
• Move to (1, 3). Energy becomes 1.
• Use medicine 2. Energy becomes 5.
• Move to (2, 3). Energy becomes 4.
• Move to (3, 3). Energy becomes 3.
• Move to (3, 4). Energy becomes 2.
• Move to (4, 4). Energy becomes 1.

There is also medicine at (2, 3) along the way, but using it will prevent him from reaching the goal.

Sample Input 2

2 2
S.
T.
1
1 2 4

Sample Output 2

No

Takahashi cannot move from the start point.

Sample Input 3

4 5
..#..
.S##.
.##T.
.....
3
3 1 5
1 2 3
2 2 1

Sample Output 3

Yes

Problem Statement

There are N 7's drawn in the first quadrant of a plane.

The i-th 7 is a figure composed of a segment connecting (x_i-1,y_i) and (x_i,y_i), and a segment connecting (x_i,y_i-1) and (x_i,y_i).

You can choose zero or more from the N 7's and delete them.

What is the maximum possible number of 7's that are wholly visible from the origin after the optimal deletion?

Here, the i-th 7 is wholly visible from the origin if and only if:

• the interior (excluding borders) of the quadrilateral whose vertices are the origin, (x_i-1,y_i), (x_i,y_i), (x_i,y_i-1) does not intersect with the other 7's.

Constraints

• 1 \leq N \leq 2 \times 10^5
• 1 \leq x_i,y_i \leq 10^9
• (x_i,y_i) \neq (x_j,y_j)\ (i \neq j)
• All values in input are integers.

Sample Input 1

3
1 1
2 1
1 2

Sample Output 1

2

If the first 7 is deleted, the other two 7's ― the second and third ones ― will be wholly visible from the origin, which is optimal.

If no 7's are deleted, only the first 7 is wholly visible from the origin.

Sample Input 2

10
414598724 87552841
252911401 309688555
623249116 421714323
605059493 227199170
410455266 373748111
861647548 916369023
527772558 682124751
356101507 249887028
292258775 110762985
850583108 796044319

Sample Output 2

10

It is best to keep all 7's.

Problem Statement

There are N points labeled 1, 2, \dots, N on the xy-plane. Point i is located at coordinates (X_i, Y_i).
You can perform the following operation between 0 and K times, inclusive.

• First, choose one of the N points. Let k be the selected point, and assume it is currently at (x, y).
• Next, choose and execute one of the following four actions:
  • Move point k along the x-axis by +1. The coordinates of point k become (x+1, y).
  • Move point k along the x-axis by -1. The coordinates of point k become (x-1, y).
  • Move point k along the y-axis by +1. The coordinates of point k become (x, y+1).
  • Move point k along the y-axis by -1. The coordinates of point k become (x, y-1).
• It is allowed to have multiple points at the same coordinates. Note that the input may already have multiple points at the same coordinates.

After all your operations, draw one square that includes all the N points inside or on the circumference, with each side parallel to the x- or y-axis.
Find the minimum possible value for the length of a side of this square. This value can be shown to be an integer since all points are always on lattice points.

In particular, if all points can be made to exist at the same coordinates, the answer is considered to be 0.

Constraints

• All input values are integers.
• 1 \le N \le 2 \times 10^5
• 0 \le K \le 4 \times 10^{14}
• 0 \le X_i, Y_i \le 10^9

Sample Input 1

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

Sample Output 1

3

The figure below illustrates this case with the horizontal x-axis and the vertical y-axis.

For example, after performing four moves following the arrows in the figure, you can include all points inside or on the circumference of the square shown in the figure with a side length of 3, and this can be shown to be the minimum value.

Sample Input 2

4 400000000000000
1000000000 1000000000
1000000000 1000000000
1000000000 1000000000
1000000000 1000000000

Sample Output 2

0

All points already exist at the same coordinates from the beginning.
For example, by performing zero operations, all points can be made to exist at the same coordinates, so the answer for this input is 0.

Sample Input 3

10 998244353
489733278 189351894
861289363 30208889
450668761 133103889
306319121 739571083
409648209 922270934
930832199 304946211
358683490 923133355
369972904 539399938
915030547 735320146
386219602 277971612

Sample Output 3

484373824