Problem:
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.

Sample Input 1

4
<><

Sample Output 1

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)

Sample Input 2

5
<<<<

Sample Output 2

1

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

(1, 2, 3, 4, 5)

Sample Input 3

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

Sample Output 3

217136290

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

Solution in Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"fmt"
	"os"
)

const Mod = int(1e9) + 7

func main() {
	N := ReadInt()
	s := ReadString()

	dp := make([][]int, N)
	for i := 0; i < N; i++ {
		dp[i] = make([]int, N)
	}
	dp[0][0] = 1

	for i := 1; i < N; i++ {
		for j := 0; j <= i; j++ {
			if s[i-1] == '<' {
				for k := 0; k < j; k++ {
					dp[i][j] += dp[i-1][k]
					dp[i][j] %= Mod
				}
			} else {
				for k := j; k <= i-1; k++ {
					dp[i][j] += dp[i-1][k]
					dp[i][j] %= Mod
				}
			}
		}
	}
	ans := 0
	for i := 0; i < N; i++ {
		ans += dp[N-1][i]
		ans %= Mod
	}
	fmt.Println(ans)
}

var reader = bufio.NewReader(os.Stdin)

func Scan(a ...interface{}) {
	if _, err := fmt.Fscan(reader, a...); err != nil {
		panic(err)
	}
}
func ReadInt() (i int)       { Scan(&i); return }
func ReadString() (s string) { Scan(&s); return }
func ReadInts(n int) []int {
	v := make([]int, n)
	for i := 0; i < n; i++ {
		Scan(&v[i])
	}
	return v
}