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()
dp = [0]*(len(s)+1)

stack = []
length = 0

for i in range (0,len(s)):

    if s[i]=='(':
        stack.append(i)
        continue

    if len(stack)==0:
        continue

    j = stack[-1]
    stack.pop()

    if j>=1:
        prev = j-1

    else:
        prev  = 0

    dp[i] = i-j+1 + dp[prev]
    
    
    if dp[i]> length:
        length = dp[i]
        count = 1

    elif dp[i]==length:
        count+=1

if length==0:
    
    print(0,1)
else:
    print(length,count)

