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)
    
    l, r, maxLen, cnt, maxCnt = 0, 0, 0, 0, 0
    for i in range(n):
        if s[i] == '(':
            l += 1
        else:
            r += 1
        if l == r:
            if 2 * r > maxLen:
                maxLen = 2 * r
                cnt = 1
            elif 2 * r == maxLen:
                cnt += 1
        elif r > l:
            l, r = 0, 0
    maxCnt = max(maxCnt, cnt)
    l, r, cnt = 0, 0, 0
    for i in range(n-1, -1, -1):
        if s[i] == '(':
            l += 1
        else:
            r += 1
            
        if l == r:
            if 2 * l > maxLen:
                maxLen = 2 * l
                cnt = 1
            elif 2 * l == maxLen:
                cnt += 1
        elif l > r:
            l, r = 0, 0

    maxCnt = max(maxCnt, cnt)

    if maxLen != 0:
        print(str(maxLen) + ' '+ str(maxCnt))
    else:
        print('0 1')
if __name__ == "__main__":
    solve()