Problem: The Balance of the World

The world should be finely balanced. Positive vs. negative, light vs. shadow, and left vs. right brackets. Your mission is to write a program that judges whether a string is balanced with respect to brackets so that we can observe the balance of the world.

A string that will be given to the program may have two kinds of brackets, round ("( )") and square ("[ ]"). A string is balanced if and only if the following conditions hold.

* For every left round bracket ("("), there is a corresponding right round bracket (")") in the following part of the string.
* For every left square bracket ("["), there is a corresponding right square bracket ("]") in the following part of the string.
* For every right bracket, there is a left bracket corresponding to it.
* Correspondences of brackets have to be one to one, that is, a single bracket never corresponds to two or more brackets.
* For every pair of corresponding left and right brackets, the substring between them is balanced.



Input

The input consists of one or more lines, each of which being a dataset. A dataset is a string that consists of English alphabets, space characters, and two kinds of brackets, round ("( )") and square ("[ ]"), terminated by a period. You can assume that every line has 100 characters or less. The line formed by a single period indicates the end of the input, which is not a dataset.

Output

For each dataset, output "yes" if the string is balanced, or "no" otherwise, in a line. There may not be any extra characters in the output.

Sample Input


So when I die (the [first] I will see in (heaven) is a score list).
[ first in ] ( first out ).
Half Moon tonight (At least it is better than no Moon at all].
A rope may form )( a trail in a maze.
Help( I[m being held prisoner in a fortune cookie factory)].
([ (([( [ ] ) ( ) (( ))] )) ]).
.
.


Output for the Sample Input


yes
yes
no
no
no
yes
yes






Example

Input




Output

Solution (in JAVA):

Solution:
import java.util.Scanner;

public class Main{
    public static void main(String[] args){
	Scanner sc = new Scanner(System.in);
	int[] f;
	int c=0, fb=0;
	f = new int[100];
	while(true){
	    String s = sc.nextLine();
	    int l = s.length();
	    if(s.charAt(0)=='.') break;
	    outer:for(int i=0;i<l;i++){
		if(s.charAt(i)=='('){
		    f[c]=0; c++; fb=1; 
		}else if(s.charAt(i)=='['){
		    f[c]=1; c++; fb=1;
		}else if(s.charAt(i)==']'){
		    f[c]=2; c++; fb=1;
		}else if(s.charAt(i)==')'){
		    f[c]=3; c++; fb=1;
		}
		while(fb==1 && c!=0 &&(f[c-1]==2 || f[c-1]==3)){
		    if(c==1) break outer;
		    else if((f[c-1]==2 && f[c-2]==1) || (f[c-1]==3 && f[c-2]==0)) c-=2;
		    else break;
		}
		fb=0;		
	    }
	    if(c==0) System.out.printf("yes\n");
	    else System.out.printf("no\n");
	    c=0;	    
	}	
    }
}