Problem: Using the given four integers from 1 to 9, we create an expression that gives an answer of 10. When you enter four integers a, b, c, d, write a program that outputs an expression that gives an answer of 10 according to the following conditions. Also, if there are multiple answers, only the first answer found will be output. If there is no answer, output 0.

* Use only addition (+), subtraction (-), and multiplication (*) as operators. Do not use division (/). You can use three operators.
* You must use all four numbers.
* You can freely change the order of the four numbers.
* You can use parentheses. You can use up to 3 sets (6) of parentheses.



Input

Given multiple datasets. The format of each dataset is as follows:


a b c d

Input ends with four 0s. The number of datasets does not exceed 40.

Output

For each dataset, combine the given four integers with the above arithmetic symbols and parentheses to output an expression or 0 with a value of 10 on one line. The expression string must not exceed 1024 characters.

Example

Input

8 7 9 9
4 4 4 4
5 5 7 5
0 0 0 0


Output

((9 * (9 - 7)) - 8)
0
((7 * 5) - (5 * 5))

Solution (in JAVA):

Solution:

import java.awt.geom.Point2D;
import java.io.*;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.Deque;
import java.util.HashMap;
import java.util.List;
import java.util.NoSuchElementException;
import java.util.PriorityQueue;
import java.util.Scanner;
public class Main {
	static boolean[] ans;
	static int[][] pass;
	static PrintWriter out = new PrintWriter(System.out);
	public static void main(String[] args) {
		
		FastScanner sc = new FastScanner();
		
		// ((a.b).(c.d))
		//(((a.b).c).d)
		//((a.(b.c)).d)
		
		char[] op = new char[]{'+','-','*'};
		int ans = 10;
		IN:while(true) {
			int[] a = new int[] {sc.nextInt(),sc.nextInt(),sc.nextInt(),sc.nextInt()};
			if(a[0] == a[1] && a[1] == a[2] && a[2] == a[3] && a[3] == 0) break;
			for(int i = 0; i < 4; i++) {
				for(int j = 0; j < 4; j++) {
					for(int k = 0; k < 4; k++) {
						for(int l = 0; l < 4; l++) {
							if(i == j || i == k || i == l || j == k || j == l || k == l) continue;
							for(int o1 = 0; o1 < 3; o1++) {
								for(int o2 = 0; o2 < 3; o2++) {
									for(int o3 = 0; o3 < 3; o3++) {
										if(c(c(a[i],a[j],o1),c(a[k],a[l],o3),o2) == ans) {
											out.println("((" + a[i]+ " " + op[o1] + " " + a[j]+ ")" + " " + op[o2] + " " + "(" + a[k] + " " + op[o3] + " " + a[l]+ "))");
											continue IN;
										}
										else if(c(c(c(a[i],a[j],o1),a[k],o2),a[l],o3) == ans) {
											out.println("(((" + a[i]+ " " + op[o1] + " " + a[j]+ ")" + " " + op[o2] + " " + "" + a[k] + ") " + op[o3] + " " + a[l]+ ")");
											continue IN;
										}
										else if(c(c(a[i],c(a[j],a[k],o2),o1),a[l],o3) == ans) {
											out.println("((" + a[i]+ " " + op[o1] + " (" + a[j]+ "" + " " + op[o2] + "" + " " + a[k] + ")) " + op[o3] + " " + a[l]+ ")");
											continue IN;
										}
									}
								}
							}
						}
					}
				}
			}
			out.println("0");
		}
		out.flush();
	}
	
	static int c(int a, int b, int c) {
		if(c == 0) {
			return a+b;
		}
		if(c == 1) {
			return a-b;
		}
		return a*b;
	}
}


		
//------------------------------//
//-----------//
class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    private void skipUnprintable() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;}
    public boolean hasNext() { skipUnprintable(); return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b)){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    
    public int nextInt() {
    	return (int)nextLong();
    }
    
    public double nextDouble() {
    	return Double.parseDouble(next());
    }
    

}