Problem: 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.

Input

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.

Output

Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".

Examples

Input

)((())))(()())


Output

6 2


Input

))(


Output

0 1

Solution (in PYTHON):

Solution:
def main():
    brackets = raw_input()
    dp_keep = [-1 for i in range(1000010)]
    stack = []
    max_seg, cnt = 0, 1

    
    for i in range(len(brackets)):
        if(brackets[i] == ')'):
            if(len(stack)):
                pos = stack.pop()
                dp_keep[i] = pos
                
                if(pos > 0  and  dp_keep[pos-1] != -1):
                    dp_keep[i] = dp_keep[pos-1]
                
            else:
               dp_keep[i] = -1
            
       
        elif(brackets[i] == '('):
            stack.append(i)
            dp_keep[i] = -1
            

    for i in range(len(brackets)):
        if(dp_keep[i] == -1):
            continue
        
        length = i - dp_keep[i] + 1

        if(length > max_seg):
            max_seg = length
            cnt = 1

        elif(length == max_seg):
            cnt += 1



    print max_seg, cnt

    
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if(__name__ == "__main__"):
    main()