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 line = readline();


var l = 0;
var la=[];
var max = 0;
var c = 0;
for(var i=0;i<line.length;i++){
	if(line[i] == '('){
		if( la[l] === undefined){
			la[l]=i;
		}
		l++;
	}else{
		l--;
		if(l>=0){
			var j = i-la[l]+1;
			if( j > max){
				max = j;
				c=1;
			}else if( j==max){
				c++;
			}
		}
		for(var k=l+1; la[k]!==undefined; k++){
			la[k]=undefined;
		}
	}
	if(l<0){
		l=0;
		la=[];
	}
}

if(max==0){
	c=1;
}
print(max+' '+c);