**These problems are from the atcoder DP contest, and were transferred onto DMOJ. All problem statements were made by several atcoder users. As there is no access to the test data, all data is randomly generated. If there are issues with the statement or data, please contact or on slack.**

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