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>.
line = input()
mx, cnt = 0, 0
stack = [0]
j = 0 
while j  < len(line) and line[j] == ")":
    j += 1
for i in range(j+1, len(line)):
    if line[i] == ")" and stack:
        stack.pop()
        if stack:
            if i + 1 - stack[-1] > mx:
                mx = i + 1 - stack[-1]
                cnt = 1
            elif i + 1 - stack[-1] == mx:
                cnt += 1
    else:
        stack.append(i + 1)

if mx == 0:
    print("0 1")
else:
    print(f"{mx} {cnt}")
    					 		 	   	  	 	   		