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 = []

for i in range(len(s)):
    if s[i] == '(':
        a.append(i)
        b.append(-1)
    else:
        if len(a) == 0:
            b.append(-1)
        else:
            x = a[len(a)-1]
            a.pop()
            if (x and s[x-1] == ')' and b[x-1] != -1):
                b.append(b[x-1])
            else:
                b.append(x)

mx = 0
c = 0
for i in range(len(b)):
    if (b[i] != -1):
        d = i - b[i] + 1
        if d == mx:
            c += 1
        if (d>mx):
            mx = d
            c = 1
        
           
print (mx,c)
            
    
