Given an array $A$ of $n$ integers, calculate:
$$
\sum_{i=1}^{n} \sum_{j=i}^{n} \text{gcd}(A_i, A_{i+1},...,A_j)
$$
### Input
- The first line contains an integer $n$.
- The next line contains $n$ integer $A_i$.
### Output
- Print the answer modulo $10^9+7$.
### Constraints
- $1 \le n \le 10^5$.
- $1 \le A_i \le 10^9$.
### Example
Input:
```
3
2 4 3
```
Output:
```
13
```
