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:
import sys

from collections import defaultdict
from time import time
from typing import Tuple

OPEN, CLOSE = '(', ')'


def magic(data: Tuple):
    open_index, open_num, step = 0, 0, 0
    chars_count = len(data) - 1
    open_indexes = []
    x = []
    while step <= chars_count:
        char = data[step]
        if char == OPEN:
            open_indexes.append(step)
            open_num += 1
        elif char == CLOSE and open_num > 0:
            open_num -= 1
            open_index = open_indexes.pop()
            yield open_index
            yield step
        step += 1
    return data


def solve(string):
    group, prev = 0, 0
    maxgroup, maxgroupcount = 0, 0
    for index in sorted(magic(tuple(string.strip()))):
        sub = index - prev
        if sub == 1 or sub == index:
            group += 1
        elif group > 0:
            if maxgroup == group: maxgroupcount += 1
            if maxgroup < group:
                maxgroup = group
                maxgroupcount = 1
            group = 1
        prev = index

    if maxgroup < group:
        maxgroup = group
        maxgroupcount = 1
    elif maxgroup == group:
        maxgroupcount += 1

    return "%s %s" % (maxgroup, maxgroupcount)


# assert solve(")((())))(()())") == "6 2"
# assert solve("))(") == "0 1"
# assert solve("()(())()") == "8 1"
# assert solve("((((()(((") == "2 1"
# assert solve("))))()())))") == "4 1"
# assert solve("(()())()(())()()())())()((()(()(())()()())((()(())()(()()()()))()(())()(((()())()(()((())()(())(()))") == "28 1"
# assert solve(")(()(((((())))))(((()))))))((()(((((((())())()))))((((((((())))((((((())))))(()((((()))))(()))))))))") == "68 1"
# start_time = time()

print(solve(sys.stdin.readline()))

# complex_input = "(()(())))()()((()(())()(()()((())))()))())((()(()(()))(()((())(())))))(()(((())(()(((()(())())))(()))()))(()()()()((((()(()()((()(()((()))())((((()()(()))())))))((())())()))(((()))()()()()()(()()(((()()))()(())))(((()))(())())(())()()(())))()()()))(()(())())))(())()))()))()()()))))))()))))()())()((()(((()(()())()()()())((((((())()))(())((()()())((())))(()()()))))(())))()()(()(())((((()()()()))))())((()()()())))((()))))()()()(()((((((()))())))((())((((()()))(())())())())()(((()()()(())(((())))())()()(((())"
# complex_input = complex_input * 10000
# print(solve(complex_input))

# print(time() - start_time)