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>.
s=input()
L=[0]*(len(s)+1)
x=0  #(
y=0  #)
l=0
stack=[]
X=[]
for i in range(len(s)):
    if s[i]==")":
        if stack!=[]:
            sp=stack.pop()
            #L[i-sp+1]+=1
            X.append([sp,i])
    else:
        stack.append(i)

while True:
    #print(X)
    #print()
    first=last=0
    XX=[]
    for a,b in X:
        if first==last:
            first,last=a,b
        elif a==last+1:
            last=b
        elif a<first and b>last:
            first,last=a,b
        else:
            XX.append([first,last])
            first,last=a,b
        #print(first,last,a,b)
    XX.append([first,last])
    if X==XX:
        break
    X=XX.copy()

for a,b in X:
    L[b-a+1]+=1

f=1
for i in range(len(s),2,-1):
    if L[i]!=0:
        print(i,L[i])
        f=0
        break
if f:
    print(0,1)
        
        
