Problem Statement

There is a grid with 10^{100} rows and 10^{100} columns.
In what follows, the cell at the i-th row from the top and j-th column from the left is denoted as cell (i,j).

In this grid, only the 100\times 100 region with cell (P,Q) as the top-left cell is painted black, and all other cells are painted white.
Determine whether cell (X,Y) is painted black.

Constraints

• 1 \leq P,Q,X,Y \leq 10000
• P,Q,X,Y are integers.

Sample Input 1

3 3
5 10

Sample Output 1

Yes

The 100\times 100 region with cell (3,3) as the top-left cell is painted black.
Cell (5,10) is included in this region, so print Yes.

Sample Input 2

5 5
10 1000

Sample Output 2

No

The 100\times 100 region with cell (5,5) as the top-left cell is painted black.
Cell (10,1000) is not included in this region, so print No.

Sample Input 3

1 2
1 1

Sample Output 3

No

The 100\times 100 region with cell (1,2) as the top-left cell is painted black.
Cell (1,1) is not included in this region, so print No.

Problem Statement

There are N bridges in AtCoder Village. The height of the bridge numbered i is H_i (i is an integer between 1 and N).
Every two different bridges in the village have different heights.

Print the number representing the highest bridge in the village.

Constraints

• 1\leq N \leq 100
• 1\leq H_i \leq 10^9
• All H_i are different.
• All values in the input are integers.

Sample Input 1

3
50 80 70

Sample Output 1

2

The village has three bridges.
The first, second, and third bridges have heights of 50, 80, and 70, respectively, so the second bridge is the highest.
Thus, 2 should be printed.

Sample Input 2

1
1000000000

Sample Output 2

1

The village has only one bridge, so the first bridge is the highest.

Sample Input 3

10
22 75 26 45 72 81 47 29 97 2

Sample Output 3

9

The village has ten bridges, and the ninth bridge (with a height of 97) is the highest.

Problem Statement

You are given N strings S_1,S_2,\ldots,S_N consisting of lowercase English letters.
Determine if there are distinct integers i and j between 1 and N, inclusive, such that the concatenation of S_i and S_j in this order is a palindrome.

A string T of length M is a palindrome if and only if the i-th character and the (M+1-i)-th character of T are the same for every 1\leq i\leq M.

Constraints

• 2\leq N\leq 100
• 1\leq \lvert S_i\rvert \leq 50
• N is an integer.
• S_i is a string consisting of lowercase English letters.
• All S_i are distinct.

Sample Input 1

5
ab
ccef
da
a
fe

Sample Output 1

Yes

If we take (i,j)=(1,4), the concatenation of S_1=ab and S_4=a in this order is aba, which is a palindrome, satisfying the condition.
Thus, print Yes.

Here, we can also take (i,j)=(5,2), for which the concatenation of S_5=fe and S_2=ccef in this order is feccef, satisfying the condition.

Sample Input 2

3
a
b
aba

Sample Output 2

No

No two distinct strings among S_1, S_2, and S_3 form a palindrome when concatenated. Thus, print No.
Note that the i and j in the statement must be distinct.

Sample Input 3

2
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa
aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Sample Output 3

Yes

Problem Statement

There are three dice, each with six faces.
The j-th face of the i-th die has A_{i,j} written on it.
For each die, each face comes up with probability \frac{1}{6}.

When these dice are rolled simultaneously, find the probability that the values 4,5,6 each appear exactly once.

Constraints

• A_{i,j} is an integer between 1 and 6, inclusive.

Sample Input 1

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

Sample Output 1

0.0277777778

The desired probability is \frac{1}{36}. An output such as 0.027778 is also accepted.

Sample Input 2

4 5 6 4 5 6
4 4 5 5 6 6
6 5 4 4 5 6

Sample Output 2

0.2222222222

The desired probability is \frac{2}{9}.

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.