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);

        while (true) {
            try {
                String s = sc.nextLine();
                if (s.equals(".")) break;
                System.out.println(search(s, 0, '.', '.', 0) == s.length()-1 ? "yes" : "no");
            } catch (Exception e) {
                break;
            }
        }
        sc.close();
    }

    private static int search(String s, int i, char shape, char opp, int depth) {
        for (; i<s.length()-1; ++i) {
            char c = s.charAt(i);
            if (opp == '.') {
                if (c == ')' || c == ']') return s.length()+10;
            }
            if (c == opp) return s.length()+10;
            else if (c == '(') i = search(s, i+1, ')', ']', depth+1);
            else if (c == '[') i = search(s, i+1, ']', ')', depth+1);
            else if (c == shape) return i;
        }
        return i + depth;
    }
}