Problem Statement

Two characters x and y are called similar characters if and only if one of the following conditions is satisfied:

• x and y are the same character.
• One of x and y is 1 and the other is l.
• One of x and y is 0 and the other is o.

Two strings S and T, each of length N, are called similar strings if and only if:

• for all i\ (1\leq i\leq N), the i-th character of S and the i-th character of T are similar characters.

Given two length-N strings S and T consisting of lowercase English letters and digits, determine if S and T are similar strings.

Constraints

• N is an integer between 1 and 100.
• Each of S and T is a string of length N consisting of lowercase English letters and digits.

Sample Input 1

3
l0w
1ow

Sample Output 1

Yes

The 1-st character of S is l, and the 1-st character of T is 1. These are similar characters.

The 2-nd character of S is 0, and the 2-nd character of T is o. These are similar characters.

The 3-rd character of S is w, and the 3-rd character of T is w. These are similar characters.

Thus, S and T are similar strings.

Sample Input 2

3
abc
arc

Sample Output 2

No

The 2-nd character of S is b, and the 2-nd character of T is r. These are not similar characters.

Thus, S and T are not similar strings.

Sample Input 3

4
nok0
n0ko

Sample Output 3

Yes

Problem Statement

You are given a sequence of integers A = (A_1, A_2, A_3).
Let B = (B_1, B_2, B_3) be any permutation of A.
Determine whether it is possible that B_1 \times B_2 = B_3.

Constraints

• All input values are integers.
• 1 \le A_1, A_2, A_3 \le 100

Sample Input 1

3 15 5

Sample Output 1

Yes

Here, A=(3,15,5). By rearranging it as B=(3,5,15), we can satisfy B_1 \times B_2 = B_3.

Sample Input 2

5 3 2

Sample Output 2

No

No permutation of B satisfies B_1 \times B_2 = B_3.

Problem Statement

You are given a string S of length N.

Find the string obtained by replacing all contiguous occurrences of na in S with nya.

Constraints

• N is an integer between 1 and 1000, inclusive.
• S is a string of length N consisting of lowercase English letters.

Sample Input 1

4
naan

Sample Output 1

nyaan

Replacing all contiguous occurrences of na in naan with nya results in the string nyaan.

Sample Input 2

4
near

Sample Output 2

near

S may not contain a contiguous na.

Sample Input 3

8
national

Sample Output 3

nyationyal

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

There are N cells, cell 1, cell 2,\ldots, cell N, arranged in a line. Cell i has an integer A_i\ (i \le A_i \le N) written on it.

For each of s=1,2,\ldots,N, solve the following problem.

• Initially, place a piece on cell s. After performing the operation "let x be the integer written on the cell where the piece is placed, and then move the piece to cell x" 10^{100} times, output the number of the cell where the piece is placed.

Constraints

• 1 \le N \le 5\times10^5
• i \le A_i \le N\ (1 \le i \le N)
• All input values are integers.

Sample Input 1

7
2 4 7 5 5 6 7

Sample Output 1

5 5 7 5 5 6 7

For s=1, the piece moves as shown in the following figure.

When the piece is placed on cell 5, the operation does not move the piece, so the answer for s=1 is 5.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

1 2 3 4 5

It is possible that the piece never moves.

Sample Input 3

15
11 3 10 7 15 10 10 11 11 13 11 12 14 14 15

Sample Output 3

11 14 14 14 15 14 14 11 11 14 11 12 14 14 15