#include <algorithm>
#include <cstring>
#include <cstdio>
using ll = long long;
constexpr int MOD = 1e9 + 7;
inline void upd(int &x, int y) { (x += y) >= MOD ? (x -= MOD) : 0; }
int arr[305], all[305][305], dp_l[155][305][305][2], dp_r[305][305][605][3];
inline int solve(int n, int off)
{
memset(all, 0, sizeof(all));
all[n][0] = 1;
for (int i = n - 1; i >= 0; i--)
{
for (int j = 0; j <= n; j++)
{
if (!all[i + 1][j])
continue;
if (arr[i] != 1 && j != n)
upd(all[i][j + 1], all[i + 1][j]);
if (arr[i] != -1 && j)
upd(all[i][j - 1], all[i + 1][j]);
}
}
memset(dp_l, 0, sizeof(dp_l));
for (int x = 0; x < n / 2; x++)
{
auto dp = dp_l[x];
dp[0][0][!x] = 1;
for (int i = 0; i < n; i++)
{
for (int j = 0; j <= x; j++)
{
for (int flg = 0; flg < 2; flg++)
{
if (!dp[i][j][flg])
continue;
if (arr[i] != 1 && j)
upd(dp[i + 1][j - 1][flg], dp[i][j][flg]);
if (arr[i] != -1 && j != x)
upd(dp[i + 1][j + 1][flg || j + 1 == x], dp[i][j][flg]);
}
}
}
}
memset(dp_r, 0, sizeof(dp_r));
for (int x = 0; x < n; x++)
{
auto dp = dp_r[x];
dp[n][0][!x] = 1;
for (int i = n - 1; i >= 0; i--)
{
for (int j = 0; j <= n; j++)
{
if (!dp[i + 1][j][0])
continue;
if (arr[i] != 1 && j < n)
upd(dp[i][j + 1][0], dp[i + 1][j][0]);
if (arr[i] != -1 && j)
upd(dp[i][j - 1][0], dp[i + 1][j][0]);
}
if (arr[i] != 1 && x)
upd(dp[i][x][1], dp[i + 1][x - 1][0]);
if (arr[i] != -1 && x < n)
upd(dp[i][x][1], dp[i + 1][x + 1][0]);
for (int j = x; j <= std::min(x * 2, n - 1); j++)
{
if (!dp[i + 1][j][1])
continue;
if (arr[i] != 1)
upd(dp[i][j + 1][1], dp[i + 1][j][1]);
if (arr[i] != -1 && j >= x + 2)
upd(dp[i][j - 1][1], dp[i + 1][j][1]);
}
}
}
int res = 0;
for (int a = 0; a <= n / 2; a++)
{
for (int b = 1; a + b <= n / 2; b++)
{
for (int pos = 0; pos < n; pos += 2)
{
if (arr[pos] == 1)
continue;
int val = a >= b ? all[pos + 1][2 * b - 1] : dp_r[a + b][pos + 1][2 * b - 1][1];
res = (res + (ll)dp_l[a][pos][0][1] * val) % MOD;
}
}
}
memset(dp_r, 0, sizeof(dp_r));
for (int x = 0; x < n / 2; x++)
{
auto dp = dp_r[x];
dp[n][n][!(x + off)] = 1;
for (int i = n - 1; i >= 0; i--)
{
for (int j = 0; j <= n; j++)
{
if (!dp[i + 1][j + n][0])
continue;
if (arr[i] != 1 && j < n)
upd(dp[i][j + 1 + n][j + 1 == x + off], dp[i + 1][j + n][0]);
if (arr[i] != -1)
upd(dp[i][j - 1 + n][0], dp[i + 1][j + n][0]);
}
for (int j = 0; j <= n; j++)
{
if (!dp[i + 1][j + n][1])
continue;
if (arr[i] != 1)
upd(dp[i][j + 1 + n][1], dp[i + 1][j + n][1]);
if (arr[i] != -1)
upd(dp[i][j - 1 + n][1 + !j], dp[i + 1][j + n][1]);
}
for (int j = -n; j <= std::min(x * 2, n - 1); j++)
{
if (!dp[i + 1][j + n][2])
continue;
if (arr[i] != 1 && j != x * 2)
upd(dp[i][j + 1 + n][2], dp[i + 1][j + n][2]);
if (arr[i] != -1 && j != -n)
upd(dp[i][j - 1 + n][2], dp[i + 1][j + n][2]);
}
}
}
for (int a = 0; a <= n / 2; a++)
{
for (int b = -n / 2 + 1; b < n / 2; b++)
{
if (a + b < 0 || a + (b < 0 ? -b : b) >= n / 2)
continue;
for (int pos = 0; pos < n; pos += 2)
{
if (arr[pos] == 1)
continue;
res = (res + (ll)dp_l[a][pos][0][1] * dp_r[a + b][pos + 1][b * 2 - 1 + n][2]) % MOD;
}
}
}
return res;
}
char str[305];
int main()
{
int n;
scanf("%d%s", &n, str);
for (int i = 0; i < n; i++)
arr[i] = str[i] == '(' ? 1 : str[i] == ')' ? -1 : 0;
int ans = solve(n, 0);
upd(ans, all[0][0]);
for (int i = 0; i < n; i++)
arr[i] *= -1;
std::reverse(arr, arr + n);
upd(ans, solve(n, 1));
printf("%d\n", ans);
return 0;
}
