Given a sequence $A_1, A_2, \ldots, A_N$ of length $N$, write a program that performs the following query:

• i j k: output the number of elements greater than $k$ in the subsequence consisting of $A_i, A_{i+1}, \ldots, A_j$.

Input

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

The second line contains $A_1, A_2, \ldots, A_N$. $(1 \le A_i \le 10^9)$

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

The next $M$ lines each contain one query $i, j, k$. $(1 \le i \le j \le N, 1 \le k \le 10^9)$

Output

For each query, output the answer on a separate line.

Examples

Input 1

5
5 1 2 3 4
3
2 4 1
4 4 4
1 5 2

Output 1

2
0
3