Given an array $A$ of $n$ integers, count the nummber of pairs of indices $i < j$ that $A_i + A_j$ is divisible by $3$.
### Input
- The first line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
### Output
- Print a single integer, which is the number of satisfied pairs.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le A_i \le 10^9$.
### Example
Input:
```
3
1 2 3
```
Output:
```
1
```
