This is yet another problem dealing with regular bracket sequences.

We should remind you that a bracket sequence is called regular, if by inserting «+» and «1» into it we can get a correct mathematical expression. For example, sequences «(())()», «()» and «(()(()))» are regular, while «)(», «(()» and «(()))(» are not. 

You are given a string of «(» and «)» characters. You are to find its longest substring that is a regular bracket sequence. You are to find the number of such substrings as well.
The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 10<sup class="upper-index">6</sup>.
S,E,F = [0] * 10, [0] * 10, [0] * 10

mx = 0
stk = []
st = input()
for i in range(len(st)):
    ch = st[i]
    if ch == '(':
        stk.append(i)
    else:
        if not stk:
            S[i] = E[i] = -1
        else:
            idx = stk.pop()
            S[i] = E[i] = idx
            if idx > 0 and st[idx-1] == ')' and S[idx-1] >=0:
                E[i] = E[idx-1]
            l = i - E[i] + 1
            F[l]+=1
            mx = max(mx,l)

    F[0] = 1
print(mx)