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>.
"""
Module which implements the search of the maximum length of balanced subsequence
of paranthesis.
"""
def max_length(array: list):
    """
    Return the maximum length of balanced subsequence of paranthesis.
    """
    max_length = 0
    num = 1
    stack = [-1]
    for i in range(len(array)):
        if array[i] == "(":
            stack.append(i)
        else:
            stack.pop()
            if stack:
                new_result = i - stack[-1]
                if new_result > max_length:
                    max_length = new_result
                    num = 1
                elif new_result == max_length:
                    num += 1
            else:
                stack.append(i)
    return (max_length, num)



if __name__ == "__main__":
    input_str = input()
    array = []
    for elem in input_str:
        array.append(elem)
    results = max_length(array)
    for elem in results:
        print(elem, end=" ")
		     	  	 	  		     	     		