##### Time limit: 0.5s

##### Memory limit: 128MB

##### Input:

##### Output:

A string $s$ is said to be *periodic* if there exists a string $t$ such that $s$ can be obtained by concatenating multiple (at least $2$) copies of $t$.

In other words, $s$ is periodic if $s = t + t + \ldots + t$ for some string $t \neq s$, where $+$ is the string concatenation operation.

You are given a string $A=\overline{a_0a_1\ldots a_{N-1}}$ of length $N$ and $Q$ queries of the form $l_i, r_i$.

For each query, determine whether the substring $A[l_i\ldots r_i] = \overline{a_{l_i}a_{l_i+1}\ldots a_{r_i}}$ is a periodic string.

# Input data

The first line contains an integer $N$. The second line contains a string $S$ of length $N$.

The third line contains an integer $Q$. The next $Q$ lines contain the values $l_i, r_i$, describing the queries.

# Output data

For each query, print *YES* if the required substring is a periodic string or *NO* if it is not.

# Constraints and clarifications

- $1 \le N, Q \le 100 \ 000$.
- $0 \le l_i \le r_i \le N - 1$.
- The string consist of lowercase letters of the English alphabet.
- For tests worth $10$ points, $N, Q \leq 100$.
- For tests worth $20$ more points, $N, Q \leq 1000$.
- For tests worth $20$ more points, $N, Q \leq 10\,000$.

# Example

`stdin`

```
14
abacbaabcabccc
5
0 13
0 3
6 11
11 13
6 10
```

`stdout`

```
NO
NO
YES
YES
NO
```

## Explanation

In the **first query**, it is asked if the whole string is periodic, so the answer is *NO*.

In the **third query**, the substring $abcabc$ is periodic, as it can be obtained by concatenating $abc$ twice.