Given an array $A$ of $n$ integers. Count the number of different arrays can be obtained by rearranging elements in $A$.
### Input
- The first line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
### Output
- Print the number of different arrays, modulo $10^9+7$..
### Constraints
- $1 \le n \le 10^6$.
- $1 \le A_i \le 10^9$.
### Example
Input:
```
4
1 2 1 3
```
Output:
```
12
```
