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

• 0 l r x: For all $l \le i \le r$, assign $A_i$ to $\max(A_i, x)$.
• 1 l r: Output $\max\left(0, \max_{l \le u \le v \le r} \left(\sum_{i=u}^{v} A_i\right)\right)$.

Input

The first line contains two integers $N$ and $Q$, representing the length of the sequence and the number of queries.

The second line contains $N$ integers $A_1, A_2, \ldots, A_N$, the initial elements of the sequence $A$.

The next $Q$ lines each describe a query in the format above.

Output

For each query of the form 1 l r, output a line with the answer.

Examples

Input 1

14 14
-3 2 1 -2 3 -4 3 -5 -1 -2 3 -5 1 5
1 3 9
0 1 14 -4
1 1 14
0 3 11 -1
1 2 8
0 3 10 -1
1 4 7
0 6 9 2
1 1 14
0 10 10 7
1 1 14
0 6 9 4
0 1 5 2
1 1 14

Output 1

3
6
7
5
18
26
39