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

• 1 i v: Change $A_i$ to $v$ ($1 \le i \le N$, $1 \le v \le 10^9$).
• 2 i j: Output the index of the minimum value among $A_i, A_{i+1}, \ldots, A_j$. If there are multiple such elements, output the one with the smallest index ($1 \le i \le j \le N$, $1 \le v \le 10^9$).

The sequence is 1-indexed.

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 $M$ of queries ($1 \le M \le 100\,000$).

The next $M$ lines each describe one query.

Output

For each query of type 2, output one answer per line in order.

Examples

Input 1

5
5 4 3 2 1
6
2 1 3
2 1 4
1 5 3
2 3 5
1 4 3
2 3 5

Output 1

3
4
4
3