Problem: 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.

Input

The first line of the input file contains a non-empty string, consisting of «(» and «)» characters. Its length does not exceed 106.

Output

Print the length of the longest substring that is a regular bracket sequence, and the number of such substrings. If there are no such substrings, write the only line containing "0 1".

Examples

Input

)((())))(()())


Output

6 2


Input

))(


Output

0 1

Solution (in PYTHON):

Solution:
def brac(s):
    fr=[0]
    stk=[[0,-1]]
    t=[]
    for i in range(len(s)):
        if len(stk)==0:
            stk.append([s[i],i])
        else:
            if s[i]=="(":
                stk.append([s[i],i])
            else:
                if stk[-1][0]=="(":
                    x=stk.pop()
                else:
                    stk.append([s[i],i])
    if stk[0][1]==0:
        stk.pop(0)
    stk.append([0,len(s)])
    for i in range(1,len(stk)):
        fr.append(stk[i][1]-stk[i-1][1]-1)
    fr.sort()
    mx=max(fr)
    cnt=0
    for i in fr:
        if i==mx:
            cnt+=1
    if mx==0:
        cnt=1
    print mx,cnt
brac(raw_input())