You are given array $A$ of $n$ integers.
There are $q$ queries of the either form:
- `1 l r`: increasing $A_l,A_{l+1},...,A_r$ by $1$.
- `2 l r`: find the number of number divisible by $3$ in subarray $A_l,A_{l+1},...,A_r$.
### Input
- The first line contains 2 integers $n, q$.
- The second line contains $n$ integers $A_i$.
- The next $q$ lines, each line contains 3 integers, a query.
### Output
- Print the answer for each query of type $2$.
### Constraints
- $1 \le n, q\le 10^5$.
- $1 \le l, r \le n$.
- $1 \le A_i \le 10^9$.
### Example
Input:
```
5 3
1 2 2 3 2
2 2 4
1 1 5
2 3 5
```
Output:
```
1
2
```
