#include <stdio.h>
#include <string.h>
#define N 300
#define MD 1000000007
void flip(char *cc, int n) {
int i, j;
char tmp;
for (i = 0; i < n; i++)
cc[i] = cc[i] == 'x' ? 'x' : (cc[i] == '(' ? ')' : '(');
for (i = 0, j = n - 1; i < j; i++, j--)
tmp = cc[i], cc[i] = cc[j], cc[j] = tmp;
}
int solve1(char *cc, int n) {
static int dp[N + 1], dq[N + 1];
int i, d;
memset(dp, 0, (n + 1) * sizeof *dp), dp[0] = 1;
for (i = 0; i < n; i++) {
memset(dq, 0, (n + 1) * sizeof *dq);
for (d = 0; d <= n; d++) {
int x = dp[d];
if (x == 0)
continue;
if (cc[i] == '(' || cc[i] == 'x')
dq[d + 1] = (dq[d + 1] + x) % MD;
if ((cc[i] == ')' || cc[i] == 'x') && d > 0)
dq[d - 1] = (dq[d - 1] + x) % MD;
}
memcpy(dp, dq, (n + 1) * sizeof *dq);
}
return dp[0];
}
int solve2(char *cc, int n) {
static int dp[N + 1][N + 1], dq[N + 1][N + 1], dq_[N + 1][N + 1], dr[N + 1][N + 1], dr_[N + 1][N + 1];
int i, d, a, a_, b, b_, ans;
for (i = 0; i <= n; i++)
memset(dp[i], 0, (n + 1) * sizeof *dp[i]);
dp[0][0] = 1;
for (i = 0; i < n; i++)
for (d = 0; d <= n; d++) {
int x = dp[i][d];
if (x == 0)
continue;
if (cc[i] == '(' || cc[i] == 'x')
dp[i + 1][d + 1] = (dp[i + 1][d + 1] + x) % MD;
if ((cc[i] == ')' || cc[i] == 'x') && d > 0)
dp[i + 1][d - 1] = (dp[i + 1][d - 1] + x) % MD;
}
for (a = 0; a <= n; a++)
for (b = 0; b <= a; b++)
dq[a][b] = dr[a][b] = 0;
dq[0][0] = 1;
ans = 0;
for (i = n - 1; i >= 0; i--) {
for (a = 0; a <= n; a++)
for (b = 0; b <= a; b++)
dq_[a][b] = dr_[a][b] = 0;
for (a = 0; a <= n; a++)
for (b = 0; b <= a; b++) {
int x = dq[a][b];
if (x == 0)
continue;
if (cc[i] == '(' || cc[i] == 'x') {
if (b > 0)
dq_[a][b - 1] = (dq_[a][b - 1] + x) % MD;
else {
for (d = 2; d <= n; d += 2)
if (a + 1 >= d / 2)
ans = (ans + (long long) dp[i][d - 1] * x) % MD;
else {
a_ = a + d / 2, b_ = d / 2 - (a + 1);
dr_[a_][b_] = (dr_[a_][b_] + x) % MD;
}
}
}
if (cc[i] == ')' || cc[i] == 'x') {
if (b < a)
dq_[a][b + 1] = (dq_[a][b + 1] + x) % MD;
else
dq_[a + 1][b + 1] = (dq_[a + 1][b + 1] + x) % MD;
}
}
for (a = 0; a <= n; a++)
for (b = 0; b <= a; b++) {
int x = dr[a][b];
if (x == 0)
continue;
if (cc[i] == '(' || cc[i] == 'x') {
if (b > 1)
dr_[a][b - 1] = (dr_[a][b - 1] + x) % MD;
else
ans = (ans + (long long) dp[i][a] * x) % MD;
}
if (cc[i] == ')' || cc[i] == 'x') {
if (b < a)
dr_[a][b + 1] = (dr_[a][b + 1] + x) % MD;
}
}
for (a = 0; a <= n; a++)
for (b = 0; b <= a; b++)
dq[a][b] = dq_[a][b], dr[a][b] = dr_[a][b];
}
return ans;
}
int solve3(char *cc, int n) {
static int dp[N + 1][N + 1], dp_[N + 1][N + 1], dq[N + 1][N + 1], dr[N + 1], dr_[N + 1], xx[2][N + 1];
int r, i, j, a, b, d, ans;
for (r = 0; r < 2; r++) {
for (a = 0; a <= n; a++)
for (b = 0; b <= a; b++)
dp[a][b] = 0;
dp[0][0] = 1;
for (i = 0; i < n; i++) {
for (a = n; a >= 0; a--)
dq[i][a] = ((a == n ? 0 : dq[i][a + 1]) + dp[a][0]) % MD;
for (a = 0; a <= n; a++)
for (b = 0; b <= a; b++)
dp_[a][b] = 0;
for (a = 0; a <= n; a++)
for (b = 0; b <= a; b++) {
int x = dp[a][b];
if (x == 0)
continue;
if (cc[i] == '(' || cc[i] == 'x') {
if (b < a)
dp_[a][b + 1] = (dp_[a][b + 1] + x) % MD;
else
dp_[a + 1][b + 1] = (dp_[a + 1][b + 1] + x) % MD;
}
if ((cc[i] == ')' || cc[i] == 'x') && b > 0)
dp_[a][b - 1] = (dp_[a][b - 1] + x) % MD;
}
for (a = 0; a <= n; a++)
for (b = 0; b <= a; b++)
dp[a][b] = dp_[a][b];
}
for (j = 0; j < n; j++) {
memset(dr, 0, (n + 1) * sizeof *dr), dr[0] = 1;
for (i = j; i >= 0; i--) {
if (cc[i] == ')' || cc[i] == 'x') {
for (d = 0; d <= n; d++)
xx[r][j + 1] = (xx[r][j + 1] + (long long) dq[i][d / 2] * dr[d]) % MD;
}
memset(dr_, 0, (n + 1) * sizeof *dr_);
for (d = 0; d <= n; d++) {
int x = dr[d];
if (x == 0)
continue;
if (cc[i] == '(' || cc[i] == 'x')
dr_[d + 1] = (dr_[d + 1] + x) % MD;
if ((cc[i] == ')' || cc[i] == 'x') && d > r)
dr_[d - 1] = (dr_[d - 1] + x) % MD;
}
memcpy(dr, dr_, (n + 1) * sizeof *dr_);
}
}
flip(cc, n);
}
ans = 0;
for (i = 1; i < n; i++)
ans = (ans + (long long) xx[0][i] * xx[1][n - i]) % MD;
return ans;
}
int main() {
static char cc[N + 1];
int n, r, ans;
scanf("%d%s", &n, cc);
if (n % 2 != 0) {
printf("0\n");
return 0;
}
ans = solve1(cc, n);
for (r = 0; r < 2; r++) {
ans = (ans + solve2(cc, n)) % MD;
flip(cc, n);
}
ans = (ans + solve3(cc, n)) % MD;
printf("%d\n", ans);
return 0;
}
