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
#!/usr/bin/env python3
import sys, math, itertools, collections, bisect
input = lambda: sys.stdin.buffer.readline().rstrip().decode('utf-8')
inf = float('inf') ;mod = 10**9+7
mans = inf ;ans = 0 ;count = 0 ;pro = 1

n = int(input())
S = input()
dp = [[0]*(n+1) for i in range(n)]
# dp[i][j] = i番目まででi番目の数字より大きい数字が残りj個の通り数
# i番目の数字より小さい数はn = i + j + kよりk = n-i-j
for j in range(n):
  dp[0][j] = 1
for i in range(n-1):
  acum = [0]*(n+1)
  for j in range(n):
    acum[j+1] = acum[j] + dp[i][j]
  for j in range(n-i-1):
    if S[i] == "<":
      dp[i+1][j] = (acum[n]-acum[j+1]) % mod
    else:
      dp[i+1][j] = (acum[j+1] - acum[0]) % mod
print(dp[n-1][0])
# print(*dp,sep = "\n")
# print(acum)
