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>.
#!/usr/bin/python3.5

S = input()
L = []

ret = 0
siz = 0

for x in S:
    if x == "(":
        L.append("(")
        siz += 1
    else:
        if len(L) == 0:
            ret = max(ret, siz)
            siz = 0
            continue

        siz += 1
        L.pop()

if len(L) == 0:
    ret = max(ret, siz)

if ret == 0:
    print("0 1")
    exit()
        
nb = 0
siz = 0
L = []

for x in S:
    if x == "(":
        L.append("(")
        siz += 1
    else:
        if len(L) == 0:
            if siz == ret:
                nb += 1
                
            siz = 0
            continue

        siz += 1
        L.pop()

if len(L) == 0 and siz == ret:
    nb += 1

print("%s %s" % (ret, nb))
