Given a sequence $A_1, A_2, \ldots, A_N$ of length $N$. Write a program to execute the following queries:

• i j: output the number of occurrences of the most frequent number among $A_i, A_{i+1}, \ldots, A_j$.

Input

The first line contains the length $N$ of the sequence $(1 \le N \le 100{,}000)$.

The second line contains $A_1, A_2, \ldots, A_N$ $(1 \le A_i \le 100{,}000)$.

The third line contains the number $M$ of queries $(1 \le M \le 100{,}000)$.

The next $M$ lines each contain a query $i, j$ $(1 \le i \le j \le n)$.

Output

For each query, output one line containing the answer.

Examples

Sample Input 1

5
1 2 1 3 3
3
1 3
2 3
1 5

Sample Output 1

2
1
2