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 JAVA):

Solution:
var i, lb = [], counter = 0, max = [0], input = readline().split('');

function update(){
    if (counter > max[0]) {
        max = [counter];
    } else if (counter && counter == max[0]) {
        max.push(counter);
    }
    counter = 0;
}

for (i = 0; i < input.length; i++){
    if (input[i] === '(') {
        lb.push(i);
    } else {
        if (lb.length) {
            input[i] = '.';
            input[lb.pop()] = '.';
        }
    }
}

for (i = 0; i < input.length; i++){
    if (input[i] === '.'){
        counter++;
    } else {
        update();
    }
}

if (counter) update();

print(max[0] + ' ' + max.length);