Find the number of strings of length $n$ that lexicographically smaller or equal to $S$ that do not contain $T$ as substring.
### Input
- The first line contains an integer $n$.
- The second line contains string $S$.
- The third line contains string $T$.
### Output
- Print the number of satisfied strings, modulo $10^9+7$.
### Constraints
- $1 \le n \le 1000$.
- $|S| = n$.
- $|T| \le |S|$.
### Example
Input:
```
1
c
b
```
Output:
```
2
```