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.util.Scanner;

public class Main{
	static BinaryOperator add = new BinaryOperator(){
		@Override
		public int apply(int left, int right){ return left + right;}
		public String toString() { return "+";}
	};
	
	static BinaryOperator subtract = new BinaryOperator(){
		@Override
		public int apply(int left, int right){ return left - right;}
		public String toString() { return "-";}
	};
	
	static BinaryOperator multiply = new BinaryOperator(){
		@Override
		public int apply(int left, int right){ return left * right;}
		public String toString() { return "*";}
	};

	static int[][] permutation4 = new int[24][4];
	static BinaryOperator[] operation = new BinaryOperator[] {add, subtract, multiply};
	static BinaryOperator[][] permutation3 = new BinaryOperator[27][3];
	
	static {
		int n = 0;
		for(int i = 0; i < 4; i++) {
			for(int j = 0; j < 4; j++) {
				if(i == j) continue;
				for(int k = 0; k < 4; k++) {
					if(i == k || j == k) continue;
					permutation4[n++] = new int[] {i, j, k, 6-i-j-k};
				}
			}
		}
		
		n = 0;
		for(int i = 0; i < 3; i++) {
			for(int j = 0; j < 3; j++) {
				for(int k = 0; k < 3; k++) {
					permutation3[n++] = new BinaryOperator[] {operation[i], operation[j], operation[k]};
				}
			}
		}
	}
	
	static FourExpression solve(int i1, int i2, int i3, int i4) {
		int[] in = new int[] {i1, i2, i3, i4};
		boolean[] bra = new boolean[] {false, true};
		for(int[] perm: permutation4) {
			for(BinaryOperator[] bp: permutation3) {
				for(boolean b: bra) {
					FourExpression result = new FourExpression(in[perm[0]], in[perm[1]], in[perm[2]], in[perm[3]], bp[0], bp[1], bp[2], b);
					if(result.calc() == 10) return result;
				}
			}
		}
		return null;
	}

	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		while(sc.hasNextInt()) {
			int arr[] = new int[] {sc.nextInt(), sc.nextInt(), sc.nextInt(), sc.nextInt()};
			if(arr[0] == 0 && arr[1] == 0 && arr[2] == 0 && arr[3] == 0) break;
			
			FourExpression out = solve(arr[0], arr[1], arr[2], arr[3]);
			if(out != null)System.out.println(out);
			else System.out.println(0);
		}
		sc.close();
	}
	
}

interface BinaryOperator{
	int apply(int left, int right);
	String toString();
}

class FourExpression{
	
	int i1, i2, i3, i4;
	BinaryOperator o1, o2, o3;
	boolean bracket;
	
	public FourExpression(int i1, int i2, int i3, int i4, BinaryOperator o1, BinaryOperator o2, BinaryOperator o3, boolean bracket){
		this.i1 = i1;
		this.i2 = i2;
		this.i3 = i3;
		this.i4 = i4;
		this.o1 = o1;
		this.o2 = o2;
		this.o3 = o3;
		this.bracket = bracket;
	}
	
	int calc(){
		return bracket? o2.apply(o1.apply(i1, i2), o3.apply(i3, i4)): o3.apply(o2.apply(o1.apply(i1, i2), i3), i4);
	}
	
	public String toString() {
		return bracket? "(" + i1 + o1.toString() + i2 +")" + o2.toString() + "(" + i3 + o3.toString() + i4 + ")":
				"((" + i1 + o1.toString() + i2 + ")" + o2.toString() + i3 + ")" + o3.toString() + i4;
	}
}