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:
import java.util.*;
import java.io.*;
import java.math.*;
public class Main{
	static int mod = (int)(1e9+7);
	public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static void main(String sp[])throws IOException{
		Scanner sc = new Scanner(System.in);
		//FastReader sc = new FastReader();
		String st = sc.next();
		int n = st.length();
		int max = Integer.MIN_VALUE;
		int count = 0;
		Stack<Integer> index = new Stack<>();
		index.push(-1);
		Stack<Character> stack = new Stack<>();
		int open =0 ;
		int close =0 ;
		for(int i=0;i<n;i++){
			char ch = st.charAt(i);
			if(st.charAt(i)=='('){
				index.push(i);
			}else{
				index.pop();
				if(index.size()==0){
					index.push(i);
				}else{
					int diff = i-index.peek();
					if(diff>max){
						max = diff;
						count=1;
					}else if(diff==max){
						count++;
					}
				}
			}			
		}
		if(max != Integer.MIN_VALUE)
			System.out.println(max+" "+count);
		else System.out.println("0 1");
 	}
	
	
	static long power(long x, long y) 
    { 
        long res = 1;      
        x = x % mod;  
  
       if (x == 0) return 0;    
  
        while (y > 0) 
        { 
            
            if((y & 1l)==1) 
                res = (res * x) % mod; 
                res = (res * x) % mod; 
      
            y = y >> 1l;  
            x = (x * x) % mod;  
        } 
        return res; 
    } 
  
	
	public static boolean prime(int n){
		int sq = (int)Math.sqrt(n);
		for(int i=2;i<=sq;i++){
			if(n%i==0)
				return false;
		}
		return true;
	}
	public static class pair{
		long bal;
		long wt;
		long diff;
	}
	
	public static class comp implements Comparator<pair>{
		public int compare(pair o1, pair o2){
			return Long.valueOf(o1.diff).compareTo(Long.valueOf(o2.diff));
		}
	}
		
	static class FastReader 
		{ 
		final private int BUFFER_SIZE = 1 << 16; 
		private DataInputStream din; 
		private byte[] buffer; 
		private int bufferPointer, bytesRead; 
  
		public FastReader() 
		{ 
			din = new DataInputStream(System.in); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 
  
		public FastReader(String file_name) throws IOException 
		{ 
			din = new DataInputStream(new FileInputStream(file_name)); 
			buffer = new byte[BUFFER_SIZE]; 
			bufferPointer = bytesRead = 0; 
		} 
  
		public String readLine() throws IOException 
		{ 
			byte[] buf = new byte[64]; // line length 
			int cnt = 0, c; 
			while ((c = read()) != -1) 
			{ 
				if (c == '\n') 
					break; 
				buf[cnt++] = (byte) c; 
			} 
			return new String(buf, 0, cnt); 
		} 
  
		public int nextInt() throws IOException 
		{ 
			int ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do
			{ 
				ret = ret * 10 + c - '0'; 
			}  while ((c = read()) >= '0' && c <= '9'); 
  
			if (neg) 
				return -ret; 
			return ret; 
		} 
  
		public long nextLong() throws IOException 
		{ 
			long ret = 0; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 
			if (neg) 
				return -ret; 
			return ret; 
		} 
  
		public double nextDouble() throws IOException 
		{ 
			double ret = 0, div = 1; 
			byte c = read(); 
			while (c <= ' ') 
				c = read(); 
			boolean neg = (c == '-'); 
			if (neg) 
				c = read(); 
  
			do { 
				ret = ret * 10 + c - '0'; 
			} 
			while ((c = read()) >= '0' && c <= '9'); 
  
			if (c == '.') 
			{ 
				while ((c = read()) >= '0' && c <= '9') 
				{ 
					ret += (c - '0') / (div *= 10); 
				} 
			} 
  
			if (neg) 
				return -ret; 
			return ret; 
		} 
  
		private void fillBuffer() throws IOException 
		{ 
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
			if (bytesRead == -1) 
				buffer[0] = -1; 
		} 
  
		private byte read() throws IOException 
		{ 
			if (bufferPointer == bytesRead) 
				fillBuffer(); 
			return buffer[bufferPointer++]; 
		} 
  
		public void close() throws IOException 
		{ 
			if (din == null) 
				return; 
			din.close(); 
		} 
	} 
}