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 = input()
a,b = 0,len(s)
while s[a]==')': a += 1
while s[b-1]=='(': b -= 1
if a==b: print(0,1); exit()

res,cnt,temp,stack = 0,1,0,0
for i in range(a,b):
    if s[i]=='(': stack += 1
    elif stack>0: 
        temp += 1; stack -= 1
        if res==temp: cnt += 1
        elif res<temp: res = temp; cnt = 1
    else: temp = 0

print(res*2,cnt)