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>.
def solve():
    s = input()
    n = len(s)
    length, cnt = 0, 0
    lCnt, rCnt = 0, 0
    for r in range(n):
        if s[r] == '(':
            lCnt += 1
        else:
            rCnt += 1
        if lCnt < rCnt:
            lCnt, rCnt = 0, 0
        elif lCnt >= rCnt:
            if rCnt == length:
                cnt += 1
            elif rCnt > length:
                length = rCnt
                cnt = 1
    if length != 0:
        print(str(length * 2) + ' '+ str(cnt))
    else:
        print('0 1')
if __name__ == "__main__":
    solve()