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 l r: Output the maximum value among all $A_i + A_j$ with $l \le i < j \le r$ ($1 \le l < r \le N$).

The indices of the sequence start from $1$.

Input

The first line contains an integer $N$, the length of the sequence ($2 \le N \le 100{,}000$).

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

The third line contains an integer $M$, the number of queries ($2 \le M \le 100{,}000$).

The next $M$ lines describe each query.

Output

For each query of type $2$, output the answer on a single line in order.

Examples

Input 1

5
5 4 3 2 1
6
2 2 4
2 1 4
1 5 5
2 3 5
1 4 9
2 3 5

Output 1

7
9
8
14