Solve in Python:
You are given a bracket sequence $s$ (not necessarily a regular one). A bracket sequence is a string containing only characters '(' and ')'.

A regular bracket sequence is a bracket sequence that can be transformed into a correct arithmetic expression by inserting characters '1' and '+' between the original characters of the sequence. For example, bracket sequences "()()" and "(())" are regular (the resulting expressions are: "(1)+(1)" and "((1+1)+1)"), and ")(", "(" and ")" are not.

Your problem is to calculate the number of regular bracket sequences of length $2n$ containing the given bracket sequence $s$ as a substring (consecutive sequence of characters) modulo $10^9+7$ ($1000000007$).


-----Input-----

The first line of the input contains one integer $n$ ($1 \le n \le 100$) — the half-length of the resulting regular bracket sequences (the resulting sequences must have length equal to $2n$).

The second line of the input contains one string $s$ ($1 \le |s| \le 200$) — the string $s$ that should be a substring in each of the resulting regular bracket sequences ($|s|$ is the length of $s$).


-----Output-----

Print only one integer — the number of regular bracket sequences containing the given bracket sequence $s$ as a substring. Since this number can be huge, print it modulo $10^9+7$ ($1000000007$).


-----Examples-----
Input
5
()))()

Output
5

Input
3
(()

Output
4

Input
2
(((

Output
0



-----Note-----

All regular bracket sequences satisfying the conditions above for the first example:   "(((()))())";  "((()()))()";  "((()))()()";  "(()(()))()";  "()((()))()". 

All regular bracket sequences satisfying the conditions above for the second example:   "((()))";  "(()())";  "(())()";  "()(())". 

And there is no regular bracket sequences of length $4$ containing "(((" as a substring in the third example.
MOD=10**9+7
n=int(input())
s=[c=='(' for c in input()]
m=len(s)
z=[[0,0]]
for v in s:
 a=z[-1][v]
 z[-1][v]=len(z)
 z.append(z[a][:])
z[m][0]=z[m][1]=m
dp=[[0 for _ in range(m+1)] for _ in range(n+1)]
dp[0][0]=1
for _ in range(2*n):
 ndp=[[0 for _ in range(m+1)] for _ in range(n+1)]
 for i in range(n+1):
  for j in range(m+1):
   if i>0:ndp[i-1][z[j][0]]=(ndp[i-1][z[j][0]]+dp[i][j])%MOD
   if i<n:ndp[i+1][z[j][1]]=(ndp[i+1][z[j][1]]+dp[i][j])%MOD
 dp=ndp
print(dp[0][m])