Given a sequence of n numbers a1, a2, ..., an and a number of k- queries. A k-query is a triple (i, j, k) (1 ≤ i ≤ j ≤ n). For each k-query (i, j, k), you have to return the number of elements greater than k in the subsequence ai, ai+1, ..., aj.
Input
- Line 1: n (1 ≤ n ≤ 30000).
- Line 2: n numbers a1, a2, ..., an (1 ≤ ai ≤ 109).
- Line 3: q (1 ≤ q ≤ 200000), the number of k- queries.
- In the next q lines, each line contains 3 numbers i, j, k representing a k-query (1 ≤ i ≤ j ≤ n, 1 ≤ k ≤ 109).
Output
- For each k-query (i, j, k), print the number of elements greater than k in the subsequence ai, ai+1, ..., aj in a single line.
Example
Input
5
5 1 2 3 4
3
2 4 1
4 4 4
1 5 2
Output
2
0
3