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Let be a positive integer. You are given a string of length , consisting of `<`

and `>`

.

Find the number of permutations of that satisfy the following condition, modulo :

- For each , if the -th character in is
`<`

and if the -th character in is`>`

.

#### Constraints

- is an integer.
- is a string of length .
- consists of
`<`

and`>`

.

#### Input Specification

The first line will contain the integer .

The second line will contain the string .

#### Output Specification

Print the number of permutations that satisfy the condition, modulo .

**Note:** Be sure to print the number modulo .

#### Sample Input 1

```
4
<><
```

#### Sample Output 1

`5`

#### Explanation For Sample 1

There are five permutations that satisfy the condition, as follows:

#### Sample Input 2

```
5
<<<<
```

#### Sample Output 2

`1`

#### Explanation For Sample 2

There is one permutation that satisfies the condition, as follows:

#### Sample Input 3

```
20
>>>><>>><>><>>><<>>
```

#### Sample Output 3

`217136290`

## Comments