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()
 
all_pair = []
stack = []
for (i, ch) in enumerate(line):
    if ch == '(':
        stack.append(i)
    else:
        if len(stack):
            left = stack.pop()
            all_pair.append((left, i))
 
all_pair.sort()
 
left = -2
right = -2
res = [0, 1]
for pair in all_pair:
    if pair[0]==right+1:
        right = pair[1]
    elif right+1 < pair[0]:
        left, right = pair
    else:
        continue
 
    length = right-left+1
    if length > res[0]:
        res = [length, 1]
    elif length == res[0]:
        res[1] += 1
 
print(res[0], res[1])

			 		   			  		   		    	 				