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>.
# cook your dish here
t = int(input())

for l in range(t):
    string = str(input())
    a = list(string)

    count = 0
    res = 0
    occur = 1
    lens = []
    for i in range(len(a)):
        if a[i]=='(':
            count+=1
        else:
            count-=1
            
            if count==0:
                res = (max(res,i+1))
                lens.append(res)
                occur+=1
            
            if count<0:
                i+=1
    if len(lens)!=0:        
        print(max(i for i in lens), occur)
    else:
        print(0,1)
    