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>.
l = input()
st = 0
a = []
lng = 0
cur = 0
cnt = 1

c = 0
for i in l:
    if (i == '('):
        break
    else:
        c += 1
        
l = l[c:]

for i in l:
    if (i == '('):
        st += 1
    else:
        st -= 1
    a.append(st)
    if (st < 0):
        if (cur > lng):
            lng = cur
            cnt = 1
        elif (cur == lng):
            cnt += 1
        cur = 0
    elif (st == 0):
        cur += 1
        if (cur > lng):
            lng = cur
            cnt = 1
        elif (cur == lng):
            cnt += 1
    else:
        cur += 1
        
print(' '.join([str(lng), str(cnt)]))