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()
st=[]
st.append(-1)
v=[]
num=0
for i in range(len(s)):
    if(s[i]=='('):
        st.append(i)
    else:
        st.pop()
        if(len(st)!=0 and num<=i-st[len(st)-1]):
            num=i-st[len(st)-1]
            v.append(num)
        if(len(st)==0):
            st.append(i)
try:
 print(max(v),' ',v.count(max(v)))
except:
 print("0  1")