Problem Statement

Given eight integers S_1,S_2,\dots, and S_8, print Yes if they satisfy all of the following three conditions, and No otherwise.

• The sequence (S_1,S_2,\dots,S_8) is monotonically non-decreasing. In other words, S_1 \leq S_2 \leq \dots \leq S_8.
• S_1,S_2,\dots, and S_8 are all between 100 and 675, inclusive.
• S_1,S_2,\dots, and S_8 are all multiples of 25.

Constraints

• 0\leq S_i \leq 1000
• All input values are integers.

Sample Input 1

125 175 250 300 400 525 600 650

Sample Output 1

Yes

They satisfy all of the three conditions.

Sample Input 2

100 250 300 400 325 575 625 675

Sample Output 2

No

They violate the first condition because S_4 > S_5.

Sample Input 3

0 23 24 145 301 413 631 632

Sample Output 3

No

They violate the second and third conditions.

Problem Statement

In the Kingdom of AtCoder, there is a standardized test of competitive programming proficiency.

An examinee will get a score out of 100 and obtain a rank according to the score, as follows:

• Novice, for a score not less than 0 but less than 40;
• Intermediate, for a score not less than 40 but less than 70;
• Advanced, for a score not less than 70 but less than 90;
• Expert, for a score not less than 90.

Takahashi took this test and got X points.

Find the minimum number of extra points needed to go up one rank higher. If, however, his rank was Expert, print expert, as there is no higher rank than that.

Constraints

• 0 \leq X \leq 100
• X is an integer.

Sample Input 1

56

Sample Output 1

14

He got 56 points and was certified as Intermediate. In order to reach the next rank of Advanced, he needs at least 14 more points.

Sample Input 2

32

Sample Output 2

8

Sample Input 3

0

Sample Output 3

40

Sample Input 4

100

Sample Output 4

expert

He got full points and was certified as Expert. There is no rank higher than that, so print expert.

Problem Statement

You are trying to implement collision detection in a 3D game.

In a 3-dimensional space, let C(a,b,c,d,e,f) denote the cuboid with a diagonal connecting (a,b,c) and (d,e,f), and with all faces parallel to the xy-plane, yz-plane, or zx-plane.
(This definition uniquely determines C(a,b,c,d,e,f).)

Given two cuboids C(a,b,c,d,e,f) and C(g,h,i,j,k,l), determine whether their intersection has a positive volume.

Constraints

• 0 \leq a < d \leq 1000
• 0 \leq b < e \leq 1000
• 0 \leq c < f \leq 1000
• 0 \leq g < j \leq 1000
• 0 \leq h < k \leq 1000
• 0 \leq i < l \leq 1000
• All input values are integers.

Sample Input 1

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

Sample Output 1

Yes

The positional relationship of the two cuboids is shown in the figure below, and their intersection has a volume of 8.

Sample Input 2

0 0 0 2 2 2
0 0 2 2 2 4

Sample Output 2

No

The two cuboids touch at a face, where the volume of the intersection is 0.

Sample Input 3

0 0 0 1000 1000 1000
10 10 10 100 100 100

Sample Output 3

Yes

Problem Statement

Note: This problem has almost the same setting as Problem F. Only the parts in bold in the main text and constraints differ.

You are holding a ring with both hands. This ring consists of N\ (N \geq 3) parts numbered 1,2,\dots,N, where parts i and i+1 (1 \leq i \leq N-1) are adjacent, and parts 1 and N are also adjacent.

Initially, your left hand is holding part 1, and your right hand is holding part 2. In one operation, you can do the following:

• Move one of your hands to an adjacent part of the part it is currently holding. However, you can do this only if the other hand is not on the destination part.

The following figure shows the initial state and examples of operations that can and cannot be made from there. The number written on each part of the ring represents the part number, and the circles labeled L and R represent your left and right hands, respectively.

You need to follow Q instructions given to you in order. The i-th (1 \leq i \leq Q) instruction is represented by a character H_i and an integer T_i, meaning the following:

• Perform some number of operations (possibly zero) so that your left hand (if H_i is L) or your right hand (if H_i is R) is holding part T_i. Here, you must not move the other hand not specified by H_i.

It is guaranteed that only achievable instructions are given.

Find the minimum total number of operations required to follow all the instructions.

Constraints

• 3 \leq N \leq 100
• 1 \leq Q \leq 100
• H_i is L or R.
• 1 \leq T_i \leq N
• N, Q, and T_i are integers.
• Only achievable instructions are given (see the problem statement for details).

Sample Input 1

6 3
R 4
L 5
R 6

Sample Output 1

8

By performing the following operations, you can follow all Q instructions in order.

1. Move your right hand as part 2 \rightarrow 3 \rightarrow 4 to follow the first instruction.
2. Move your left hand as part 1 \rightarrow 6 \rightarrow 5 to follow the second instruction.
3. Move your right hand as part 4 \rightarrow 3 \rightarrow 2 \rightarrow 1 \rightarrow 6 to follow the third instruction.

In this case, the total number of operations is 2+2+4=8, which is the minimum. (Note that when following the third instruction, you cannot move your right hand as part 4 \rightarrow 5 \rightarrow 6.)

Sample Input 2

100 2
L 1
R 2

Sample Output 2

0

There are cases where you can follow the instructions without performing any operations.

Sample Input 3

30 8
R 23
R 26
R 29
L 20
R 29
R 19
L 7
L 16

Sample Output 3

92

Problem Statement

How many integer sequences of length N, A=(A_1, \ldots, A_N), satisfy all of the conditions below?

• 1\le A_i \le M (1 \le i \le N)

• \displaystyle\sum _{i=1}^N A_i \leq K

Since the count can get enormous, find it modulo 998244353.

Constraints

• 1 \leq N, M \leq 50
• N \leq K \leq NM
• All values in input are integers.

Sample Input 1

2 3 4

Sample Output 1

6

The following six sequences satisfy the conditions.

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

Sample Input 2

31 41 592

Sample Output 2

798416518

Be sure to print the count modulo 998244353.