BR1

#include<bits/stdc++.h>
using namespace std;

const int nmax = 5011, base = 1e9 + 7;

int n;
int f[nmax][nmax][2];
char A[nmax];

int dp(int i, int d, int ok){
    if (i == n) return d==0;
    auto &r = f[i][d][ok];
    if (r != -1) return r;
    r = 0;
    for (char c : {'(', ')'}){
        if ((c <= A[i] || ok) && (d > 0 || c == '('))
            r += dp(i+1, d + (c=='('?1:-1), ok || c < A[i]);
    }
    r %= base;
    return r;
}

int32_t main(){
    scanf("%s", A);
    n = strlen(A);
    memset(f,255,sizeof(f));
    cout << dp(0, 0, 0);
}