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:
bs = raw_input()

dp = [0] * len(bs)

for i in xrange(1, len(bs)):
    if bs[i] == ')':
        if bs[i-1] == '(':
            pre = dp[i-2] if i>=2 else 0
            dp[i] = pre + 2
        elif (i-dp[i-1])>=1 and bs[i-dp[i-1]-1] == '(':
            pre = dp[i-dp[i-1]-2] if (i-dp[i-1])>=2 else 0
            dp[i] = pre + dp[i-1] + 2

maxv = 0
num = 0
for v in dp:
    if v > maxv:
        maxv = v
        num = 1
    elif v == maxv:
        num += 1

print maxv, num if maxv>0 else 1