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 PYTHON3):

Solution:
s = input()
dp, m, c, mx = [0], {0:-1}, 0, 0
for i in range(len(s)):
    if s[i] == '(':
        dp.append(0)
        c += 1
    else:
        c -= 1
        j = m.get(c, -2)
        if j == -2:
            dp.append(0)
        else:
            dp.append(dp[j + 1] + i - j)
        mx = max(mx, dp[-1])
    m[c] = i
print(*[mx, dp.count(mx)] if mx else "01")