Given an array $A$ of $n$ elements, there are $q$ queries, each falling into one of two types:
- `1 i x`: Assign the value $x$ to $A_i$.
- `2 l r x`: Count the number of pairs $(i, j)$ such that $l \le i \le j \le r$ and the maximum value in the subarray $A_{i...j}$ does not exceed $x$.
Answer the queries of type $2$.
### Input
- The first line contains two integers $n, q$.
- The second line contains $n$ integers $A_i$.
- The next $q$ lines each contain a query in the specified format.
### Output
- Print an integer as the answer for each query of type $2$.
### Constraints
- $1 \le n,q \le 10^5$.
- $1 \le A_i,x \le 10^9$.
- $1 \le l \le r \le n$.
### Example
Input:
```
6 6
1 1 4 5 1 4
1 1 4
2 1 4 2
2 1 1 4
2 1 5 4
1 5 4
2 3 3 3
```
Output:
```
1
1
7
0
```
