Kristina has an array $a$, called a template, consisting of $n$ integers. She also has $m$ strings, each consisting only of lowercase Latin letters. The strings are numbered from $1$ to $m$. She wants to check which strings match the template.

A string $s$ is considered to match the template if all of the following conditions are simultaneously satisfied:

• The length of the string $s$ is equal to the number of elements in the array $a$.
• The same numbers from $a$ correspond to the same symbols from $s$. So, if $a_i = a_j$, then $s_i = s_j$ for ($1 \le i, j \le n$).
• The same symbols from $s$ correspond to the same numbers from $a$. So, if $s_i = s_j$, then $a_i = a_j$ for ($1 \le i, j \le n$).

In other words, there must be a one-to-one correspondence between the characters of the string and the elements of the array.

For example, if $a$ = [$3, 5, 2, 1, 3$], then the string "abfda" matches the template, while the string "afbfa" does not, since the character "f" corresponds to both numbers $1$ and $5$.

Input

The first line of input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The following descriptions are for the test cases.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the number of elements in the array $a$.

The second line of each test case contains exactly $n$ integers $a_i$ ($-10^9 \le a_i \le 10^9$) — the elements of the array $a$.

The third line of each test case contains a single integer $m$ ($1 \le m \le 2 \cdot 10^5$) — the number of strings to check for template matching.

Following are $m$ strings, each containing a non-empty string $s_j$ ($1 \le |s_j| \le 2 \cdot 10^5$), consisting of lowercase Latin letters.

It is guaranteed that the sum of $n$ across all test cases does not exceed $2 \cdot 10^5$, and that the sum of the lengths of all strings does not exceed $2 \cdot 10^5$.

Output

For each test case, output $m$ lines. On the $i$-th line ($1 \le i \le m$) output:

• "YES", if the string with index $i$ matches the template;
• "NO" otherwise.

You may output the answer in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as a positive answer).

Note

The first test case is explained in the problem statement.

Samples

3
5
3 5 2 1 3
2
abfda
afbfa
2
1 2
3
ab
abc
aa
4
5 -3 5 -3
4
aaaa
bcbc
aba
cbcb

YES
NO
YES
NO
NO
NO
YES
NO
YES