Problem Statement

You are given an integer N. If N is between -2^{31} and 2^{31}-1 (inclusive), print Yes; otherwise, print No.

Constraints

• -2^{63} \leq N < 2^{63}
• N is an integer.

Sample Input 1

10

Sample Output 1

Yes

10 is between -2^{31} and 2^{31}-1, so Yes should be printed.

Sample Input 2

-9876543210

Sample Output 2

No

-9876543210 is less than -2^{31}, so No should be printed.

Sample Input 3

483597848400000

Sample Output 3

No

483597848400000 is greater than 2^{31}-1, so No should be printed.

Problem Statement

You are given a string S, which represents a weather forecast for the seven days starting tomorrow.
The i-th of those seven days is forecast to be sunny if the i-th character of S is o, and rainy if that character is x.

Tell us whether the N-th day is forecast to be sunny.

Constraints

• N is an integer between 1 and 7 (inclusive).
• S is a string of length 7 consisting of o and x.

Sample Input 1

4
oooxoox

Sample Output 1

No

The forecast for each of the seven days starting tomorrow is as follows: sunny, sunny, sunny, rainy, sunny, sunny, rainy.
In particular, the fourth day is forecast to be rainy.

Sample Input 2

7
ooooooo

Sample Output 2

Yes

Problem Statement

You are given N-by-N matrices A and B where each element is 0 or 1.
Let A_{i,j} and B_{i,j} denote the element at the i-th row and j-th column of A and B, respectively.
Determine whether it is possible to rotate A so that B_{i,j} = 1 for every pair of integers (i, j) such that A_{i,j} = 1.
Here, to rotate A is to perform the following operation zero or more times:

• for every pair of integers (i, j) such that 1 \leq i, j \leq N, simultaneously replace A_{i,j} with A_{N + 1 - j,i}.

Constraints

• 1 \leq N \leq 100
• Each element of A and B is 0 or 1.
• All values in the input are integers.

Sample Input 1

3
0 1 1
1 0 0
0 1 0
1 1 0
0 0 1
1 1 1

Sample Output 1

Yes

Initially, A is :

0 1 1
1 0 0
0 1 0

After performing the operation once, A is :

0 1 0
1 0 1 
0 0 1

After performing the operation once again, A is :

0 1 0
0 0 1
1 1 0

Here, B_{i,j} = 1 for every pair of integers (i, j) such that A_{i,j} = 1, so you should print Yes.

Sample Input 2

2
0 0
0 0
1 1
1 1

Sample Output 2

Yes

Sample Input 3

5
0 0 1 1 0
1 0 0 1 0
0 0 1 0 1
0 1 0 1 0
0 1 0 0 1
1 1 0 0 1
0 1 1 1 0
0 0 1 1 1
1 0 1 0 1
1 1 0 1 0

Sample Output 3

No

Problem Statement

Takahashi ate N plates of sushi at a sushi restaurant. The color of the i-th plate is represented by a string C_i.

The price of a sushi corresponds to the color of the plate. For each i=1,\ldots,M, the sushi on a plate whose color is represented by a string D_i is worth P_i yen a plate (yen is the currency of Japan). If the color does not coincide with any of D_1,\ldots, and D_M, it is worth P_0 yen a plate.

Find the total amount of the prices of sushi that Takahashi ate.

Constraints

• 1\leq N,M\leq 100
• C_i and D_i are strings of length between 1 and 20, inclusive, consisting of lowercase English letters.
• D_1,\ldots, and D_M are distinct.
• 1\leq P_i\leq 10000
• N, M, and P_i are integers.

Sample Input 1

3 2
red green blue
blue red
800 1600 2800

Sample Output 1

5200

A blue plate, red plate, and green plate are worth P_1 = 1600, P_2 = 2800, and P_0 = 800 yen, respectively.

The total amount of the prices of the sushi that he ate is 2800+800+1600=5200 yen.

Sample Input 2

3 2
code queen atcoder
king queen
10 1 1

Sample Output 2

21

Problem Statement

On a two-dimensional plane, Takahashi is initially at point (0, 0), and his initial health is H. M items to recover health are placed on the plane; the i-th of them is placed at (x_i,y_i).

Takahashi will make N moves. The i-th move is as follows.

1. Let (x,y) be his current coordinates. He consumes a health of 1 to move to the following point, depending on S_i, the i-th character of S:

   • (x+1,y) if S_i is R;
   • (x-1,y) if S_i is L;
   • (x,y+1) if S_i is U;
   • (x,y-1) if S_i is D.

2. If Takahashi's health has become negative, he collapses and stops moving. Otherwise, if an item is placed at the point he has moved to, and his health is strictly less than K, then he consumes the item there to make his health K.

Determine if Takahashi can complete the N moves without being stunned.

Constraints

• 1\leq N,M,H,K\leq 2\times 10^5
• S is a string of length N consisting of R, L, U, and D.
• |x_i|,|y_i| \leq 2\times 10^5
• (x_i, y_i) are pairwise distinct.
• All values in the input are integers, except for S.

Sample Input 1

4 2 3 1
RUDL
-1 -1
1 0

Sample Output 1

Yes

Initially, Takahashi's health is 3. We describe the moves below.

• 1-st move: S_i is R, so he moves to point (1,0). His health reduces to 2. Although an item is placed at point (1,0), he do not consume it because his health is no less than K=1.

• 2-nd move: S_i is U, so he moves to point (1,1). His health reduces to 1.

• 3-rd move: S_i is D, so he moves to point (1,0). His health reduces to 0. An item is placed at point (1,0), and his health is less than K=1, so he consumes the item to make his health 1.

• 4-th move: S_i is L, so he moves to point (0,0). His health reduces to 0.

Thus, he can make the 4 moves without collapsing, so Yes should be printed. Note that the health may reach 0.

Sample Input 2

5 2 1 5
LDRLD
0 0
-1 -1

Sample Output 2

No

Initially, Takahashi's health is 1. We describe the moves below.

• 1-st move: S_i is L, so he moves to point (-1,0). His health reduces to 0.

• 2-nd move: S_i is D, so he moves to point (-1,-1). His health reduces to -1. Now that the health is -1, he collapses and stops moving.

Thus, he will be stunned, so No should be printed.

Note that although there is an item at his initial point (0,0), he does not consume it before the 1-st move, because items are only consumed after a move.