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_idx = list()
dp = [0] * len(s)

max_v = 0
for i in range(len(s)):
    #print(i, l_idx)
    if s[i] == '(':
        l_idx.append(i)
    else:
        now = 0
        if len(l_idx) > 0:
            now = 2
            if l_idx[-1] > 0:
                now += dp[l_idx[-1]-1]
            if i > 0:
                now += dp[i-1]
            l_idx.pop()
        dp[i] = now
        max_v = max(now, max_v)

#print(dp)
if max_v == 0:
    print(0, 1)
else:
    num = dp.count(max_v)
    print(max_v, num)