Score : $100$ points

Problem Statement

Let $N$ be a positive integer. You are given a string $s$ of length $N - 1$, consisting of < and >.

Find the number of permutations $(p_1, p_2, \ldots, p_N)$ of $(1, 2, \ldots, N)$ that satisfy the following condition, modulo $10^9 + 7$:

• For each $i$ ($1 \leq i \leq N - 1$), $p_i < p_{i + 1}$ if the $i$-th character in $s$ is <, and $p_i > p_{i + 1}$ if the $i$-th character in $s$ is >.

Constraints

• $N$ is an integer.
• $2 \leq N \leq 3000$
• $s$ is a string of length $N - 1$.
• $s$ consists of < and >.

Input

Input is given from Standard Input in the following format:

$N$

$s$

Output

Print the number of permutations that satisfy the condition, modulo $10^9 + 7$.

4
<><

5

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

• $(1, 3, 2, 4)$
• $(1, 4, 2, 3)$
• $(2, 3, 1, 4)$
• $(2, 4, 1, 3)$
• $(3, 4, 1, 2)$

5
<<<<

1

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

• $(1, 2, 3, 4, 5)$

20
>>>><>>><>><>>><<>>

217136290

Be sure to print the number modulo $10^9 + 7$.