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 C++ (GCC 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <iomanip>
#include <string>
#include <stack>
#include <vector>
#include <complex>
#include <math.h>
#include <stdio.h>
#include <algorithm>
#include <utility>
#include <functional>
#include <iterator>
#include <map>
#include <set>
#include <queue>
#include <list>
#include <regex>
#include <limits>
#include <time.h>
#include <cstdint>
#include <unordered_map>
#include <unordered_set>
#include <bitset>
#include <limits.h>
using namespace std;
using pii  = pair<int,int>;
using ll=long long;
using ld=long double;
#define pb push_back
#define mp make_pair
#define sc second
#define fr first
#define stpr setprecision
#define cYES cout<<"YES"<<endl
#define cNO cout<<"NO"<<endl
#define cYes cout<<"Yes"<<endl
#define cNo cout<<"No"<<endl
#define rep(i,n) for(ll i=0;i<(n);++i)
#define Rep(i,a,b) for(ll i=(a);i<(b);++i)
#define rrep(i,n) for(ll i=n-1;i>=0;i--)
#define rRep(i,a,b) for(ll i=a;i>=b;i--)
#define crep(i) for(char i='a';i<='z';++i)
#define psortsecond(A,N) sort(A,A+N,[](const pii &a, const pii &b){return a.second<b.second;});
#define ALL(x) (x).begin(),(x).end()
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define endl '\n'
int ctoi(const char c){
  if('0' <= c && c <= '9') return (c-'0');
  return -1;
}
ll gcd(ll a,ll b){return (b == 0 ? a : gcd(b, a%b));}
ll lcm(ll a,ll b){return a*b/gcd(a,b);}
constexpr ll MOD=1000000007;
constexpr ll INF=1000000011;
constexpr ll MOD2=998244353;
constexpr ll LINF = 1001002003004005006ll;
constexpr ld EPS=10e-8;
template <class T, class U> inline bool chmax(T& lhs, const U& rhs) { if (lhs < rhs) { lhs = rhs; return 1; } return 0; }
template <class T, class U> inline bool chmin(T& lhs, const U& rhs) { if (lhs > rhs) { lhs = rhs; return 1; } return 0; }
template<typename T> istream& operator>>(istream& is,vector<T>& v){for(auto&& x:v)is >> x;return is;}
template<typename T,typename U> istream& operator>>(istream& is, pair<T,U>& p){ is >> p.first; is >> p.second; return is;}
template<typename T,typename U> ostream& operator>>(ostream& os, const pair<T,U>& p){ os << p.first << ' ' << p.second; return os;}
template<class T> ostream& operator<<(ostream& os, vector<T>& v){
  for(auto i=begin(v); i != end(v); ++i){
    if(i !=begin(v)) os << ' ';
    os << *i;
  }
  return os;
}

template <std::uint_fast64_t Modulus> class modint {
  using u64 = std::uint_fast64_t;

public:
  u64 a;

  constexpr modint(const u64 x = 0) noexcept : a(x % Modulus) {}
  constexpr u64 &value() noexcept { return a; }
  constexpr const u64 &value() const noexcept { return a; }
  constexpr modint operator+(const modint rhs) const noexcept {
    return modint(*this) += rhs;
  }
  constexpr modint operator-(const modint rhs) const noexcept {
    return modint(*this) -= rhs;
  }
  constexpr modint operator*(const modint rhs) const noexcept {
    return modint(*this) *= rhs;
  }
  constexpr modint operator/(const modint rhs) const noexcept {
    return modint(*this) /= rhs;
  }
  constexpr modint &operator+=(const modint rhs) noexcept {
    a += rhs.a;
    if (a >= Modulus) {
      a -= Modulus;
    }
    return *this;
  }
  constexpr modint &operator-=(const modint rhs) noexcept {
    if (a < rhs.a) {
      a += Modulus;
    }
    a -= rhs.a;
    return *this;
  }
  constexpr modint &operator*=(const modint rhs) noexcept {
    a = a * rhs.a % Modulus;
    return *this;
  }
  constexpr modint &operator/=(modint rhs) noexcept {
    u64 exp = Modulus - 2;
    while (exp) {
      if (exp % 2) {
        *this *= rhs;
      }
      rhs *= rhs;
      exp /= 2;
    }
    return *this;
  }
};

modint<MOD> dp[3007][3007];
string S;

int main(){
  ll N;
  cin >> N >> S;
  rep(i,N){
    dp[0][i]=1;
  }
  rep(i,S.size()){
    if(S[i]=='<'){
      modint<MOD> sum=0;
      rep(j,N-i-1){
        sum+=dp[i][j];
        dp[i+1][j]=sum;
      }
    }
    else{
      modint<MOD> sum=0;
      rRep(j,N-i,1){
        sum+=dp[i][j];
        dp[i+1][j-1]=sum;
      }
    }
  }
  cout << dp[N-1][0].a << endl;
}