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>.
if __name__ == "__main__":
    cadena = input()
    pila = []
    count = length = actual = 0
    maybe = False
    dp = [-1]*len(cadena)
    for i in range(len(cadena)):
        if cadena[i] == '(':
            pila.append('(')
        elif cadena[i] == ')':
            if len(pila)>0:
                dp[i] = len(pila)
                pila.pop()

    for i in range(len(dp)):
        if dp[i] != -1:
            actual += 2
        if dp[i] == 1:
            length = max(length,actual)
            actual = 0
            count += 1

    if len(pila) > 0 and (length != 0 or actual != 0):
        count += 1
        length = max(length,actual)

    if length == 0 and count == 0:
        print(0,1)
    else:
        print(length,count)
 	 		 				    		  	 	     	   	