A sequence $A_1, A_2, \ldots, A_N$ of length $N$ is given. Write a program to execute 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 minimum value among $A_i, A_{i+1}, \ldots, A_j$. ($1 \le i \le j \le N$)

The sequence is 1-indexed.

Input

The first line contains the size $N$ 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 contain a query.

Output

For each type-2 query, output the answer on its own 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
2
2
3