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>.
import sys
from math import gcd
 
input = lambda: sys.stdin.readline().strip()
# for i in range(int(input())):09R5LVGFMTARSVNG77
#     n,x = map(int,input().split())
slov = {')': -1, '(': 1}
s = list(map(lambda x: slov[x], input()))
b = []
ans = 0
k = 1
for i in range(len(s)):
    f = False
    if b:
        if s[i]==1:
            b.append((s[i],i))
        elif b[-1][0]==1:
            t,ind = b.pop()
            if ans<i-ind+1:
                ans = i-ind+1
                k=1
            elif ans == i-ind+1:
                k+=1
    else:
        b.append((s[i],i))
 
    # print(b,ans,f)
if len(b):
    print(ans,k)
else:
    print(len(s),1)