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.

Examples

Input

4
<><


Output

5


Input

5
<<<<


Output

1


Input

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


Output

217136290
from sys import stdin
import sys
import math
from functools import reduce
import functools
import itertools
from collections import deque,Counter,defaultdict
from operator import mul
import copy
# ! /usr/bin/env python
# -*- coding: utf-8 -*-
import heapq
sys.setrecursionlimit(10**6)
INF =  float("inf")
import bisect
import statistics
mod = 10**9+7

N = int(input())
s = input()

dp = [[0 for j in range(N+1)] for i in range(N+1)]
for j in range(1,N+1):
    dp[1][j] = 1

for i in range(2,N+1):
    a = [0 for i in range(N-i+3)]
    for k in range(1,N-i+3):
        a[k] = (a[k-1] + dp[i-1][k]) % mod

    for j in range(1,N-i+2):
        if s[i-2] == "<":
            dp[i][j] = (a[N-i+2] - a[j]) % mod
            # for k in range(1,N-i-j+3):
            #     dp[i][j] = (dp[i][j] + dp[i-1][j+k]) % mod
        else:
            dp[i][j] = (a[j] - a[0]) % mod
            # for k in range(1,j+1):
            #     dp[i][j] = (dp[i][j] + dp[i-1][k]) % mod

print(dp[N][1] % mod)