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.io.IOException;
import java.lang.reflect.Array;
import java.util.*;

class Main {
	public static void main(String[] args) throws Exception {
		Scanner in = new Scanner(System.in);
		while(in.hasNext()) {
			List<Integer> ints = new ArrayList<>();
			ints.add(in.nextInt());
			ints.add(in.nextInt());
			ints.add(in.nextInt());
			ints.add(in.nextInt());
			if(ints.get(0) == 0) return;
			System.out.println(solve(ints));
		}
	}

	/**
	 * http://dai1741.github.io/maximum-algo-2012/docs/parsing/
	 */
	static class Calc {
		int i;
		String s;
		private static final Map<String, Integer> opPriority = new HashMap<String, Integer>() {
			{
				put("+", 2);
				put("-", 2);
				put("*", 3);
				put("(", 3);
				put(")", 3);
			}
		};

		public boolean isOperator(String token) {
			return opPriority.containsKey(token);
		}

		public int calc(String exp) throws Exception {
			i=0;
			s = exp;
			s = s.replaceAll(" ", "");
			return expr();
		}

		public int expr() throws Exception {
			int val = term();
			while(i < s.length() && (s.charAt(i) == '+' || s.charAt(i) == '-')) {
				char op = s.charAt(i);
				i++;
				int val2 = term();
				if (op == '+') val += val2;
				else val -= val2;
			}
			return val;
		}

		public int term() throws Exception {
			int val = factor();
			while(i < s.length() && s.charAt(i) == '*') {
				char op = s.charAt(i);
				i++;
				int val2 = factor();
				val *= val2;
			}
			return val;
		}

		public int factor() throws Exception {
			if(Character.isDigit(s.charAt(i))) {
				return number();
			}

			if(s.charAt(i) != '(') {
				new Exception();
			}
			i++;
			int ret = expr();
			if(s.charAt(i) != ')') {
				new Exception();
			}
			i++;
			return ret;
		}

		public int number() throws Exception {
			int n = Integer.parseInt(""+s.charAt(i));
			i++;
			while(i < s.length() && Character.isDigit(s.charAt(i))) {
				n = n * 10 + Integer.parseInt(""+s.charAt(i));
				i++;
			}
			return n;
		}
	};

	public static String solve(List<Integer> ints) throws Exception {
		String[] exps={
				"(a x a) x a x a",
				"(a x a x a) x a",
				"((a x a) x a) x a",
				"(a x (a x a)) x a",
				"a x (a x a) x a",
				"a x (a x a x a)",
				"a x ((a x a) x a)",
				"a x (a x (a x a))",
				"a x a x (a x a)",
				"(a x a) x (a x a)"
		};
		String[] ops = {"+","-","*"};
		for(int a=0;a<4;a++) {
			for(int b=0;b<4;b++) {
				if(a == b) continue;
				for(int c=0;c<4;c++) {
					if(a == c || b == c) continue;
					for(int d=0;d<4;d++) {
						if(a == d || b == d || c == d) continue;
						for(int e=0;e<3;e++) {
							for(int f=0;f<3;f++) {
								for (int g = 0; g < 3; g++) {
									for (int i = 0; i < exps.length; i++) {
										String exp = exps[i];
										String buf = new String(exp);
										buf = buf.substring(0, buf.indexOf('a')) + ints.get(a) + buf.substring(buf.indexOf('a')+1);
										buf = buf.substring(0, buf.indexOf('a')) + ints.get(b) + buf.substring(buf.indexOf('a')+1);
										buf = buf.substring(0, buf.indexOf('a')) + ints.get(c) + buf.substring(buf.indexOf('a')+1);
										buf = buf.substring(0, buf.indexOf('a')) + ints.get(d) + buf.substring(buf.indexOf('a')+1);
										buf = buf.substring(0, buf.indexOf('x')) + ops[e] + buf.substring(buf.indexOf('x')+1);
										buf = buf.substring(0, buf.indexOf('x')) + ops[f] + buf.substring(buf.indexOf('x')+1);
										buf = buf.substring(0, buf.indexOf('x')) + ops[g] + buf.substring(buf.indexOf('x')+1);
										if((new Calc().calc(buf)) == 10) {
											return buf;
										}
									}
								}
							}
						}
					}
				}
			}
		}
		return "0";
	}
}