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

• 1 i j k: Output the number of elements greater than $k$ in the subsequence formed by $A_i, A_{i+1}, \ldots, A_j$.
• 2 i k: Change $A_i$ to $k$.

The indices of the sequence start from 1.

Input

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

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

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

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

Output

For each query of type 1, output the answer on a line.

Examples

Input 1

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

Output 1

2
1
4