Number Replacement

2000ms

262144K

Description:

An integer array $$$a_1, a_2, \ldots, a_n$$$ is being transformed into an array of lowercase English letters using the following prodecure:

While there is at least one number in the array:

Choose any number $$$x$$$ from the array $$$a$$$, and any letter of the English alphabet $$$y$$$.
Replace all occurrences of number $$$x$$$ with the letter $$$y$$$.

For example, if we initially had an array $$$a = [2, 3, 2, 4, 1]$$$, then we could transform it the following way:

Choose the number $$$2$$$ and the letter c. After that $$$a = [c, 3, c, 4, 1]$$$.
Choose the number $$$3$$$ and the letter a. After that $$$a = [c, a, c, 4, 1]$$$.
Choose the number $$$4$$$ and the letter t. After that $$$a = [c, a, c, t, 1]$$$.
Choose the number $$$1$$$ and the letter a. After that $$$a = [c, a, c, t, a]$$$.

After the transformation all letters are united into a string, in our example we get the string "cacta".

Having the array $$$a$$$ and the string $$$s$$$ determine if the string $$$s$$$ could be got from the array $$$a$$$ after the described transformation?

Input:

The first line contains a single integer $$$t$$$ $$$(1 \leq t \leq 10^3$$$) — the number of test cases.

Then the description of the test cases follows.

The first line of each test case contains a single integer $$$n$$$ ($$$1 \leq n \leq 50$$$) — the length of the array $$$a$$$ and the string $$$s$$$.

The second line of each test case contains exactly $$$n$$$ integers: $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \leq a_i \leq 50$$$) — the elements of the array $$$a$$$.

The third line of each test case contains a string $$$s$$$ of length $$$n$$$, consisting of lowercase English letters.

Output:

For each test case, output "YES", if we can get the string $$$s$$$ from the array $$$a$$$, and "NO" otherwise. You can output each letter in any case.

Sample Input:

7
5
2 3 2 4 1
cacta
1
50
a
2
11 22
ab
4
1 2 2 1
aaab
5
1 2 3 2 1
aaaaa
6
1 10 2 9 3 8
azzfdb
7
1 2 3 4 1 1 2
abababb

Sample Output:

YES
YES
YES
NO
YES
YES
NO

Note:

The first test case corresponds to the sample described in the statement.

In the second test case we can choose the number $$$50$$$ and the letter a.

In the third test case we can choose the number $$$11$$$ and the letter a, after that $$$a = [a, 22]$$$. Then we choose the number $$$22$$$ and the letter b and get $$$a = [a, b]$$$.

In the fifth test case we can change all numbers one by one to the letter a.

Informação

Provedor Codeforces

Código CF1744A