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.*;

class Main {
	Scanner sc = new Scanner(System.in);

	public int solve(int l, int r, int op) {
		switch (op) {
		case 0:
			return l + r;
		case 1:
			return l - r;
		case 2:
			return l * r;
		default:
			return 0;
		}
	}

	public char op(int op) {
		switch (op) {
		case 0:
			return '+';
		case 1:
			return '-';
		case 2:
			return '*';
		default:
			return 0;
		}
	}

	public void run() {
		while (true) {
			int vals[] = new int[] { sc.nextInt(), sc.nextInt(), sc.nextInt(),
					sc.nextInt() };
			if (Arrays.equals(vals, new int[] { 0, 0, 0, 0 })) {
				break;
			}

			PermutationList pl = new PermutationList(4);

			boolean isset=false;
			end: for (int[] per : pl) {
				for (int op0 = 0; op0 < 3; op0++)
					for (int op1 = 0; op1 < 3; op1++)
						for (int op2 = 0; op2 < 3; op2++) {
							if (solve(
									solve(solve(vals[per[0]], vals[per[1]], op0),
											vals[per[2]], op1), vals[per[3]],
									op2) == 10) {
								ln("(((" + vals[per[0]] + " " + op(op0) + " "
										+ vals[per[1]] + ")" + " " + op(op1)
										+ " " + vals[per[2]] + ")" + " "
										+ op(op2) + " " + vals[per[3]] + ")");
								isset=true;
								break end;
							}
							if (solve(
									solve(vals[per[0]],solve(vals[per[1]],vals[per[2]], op1), op0),
											vals[per[3]],
									op2) == 10) {
								ln("((" + vals[per[0]] + " " + op(op0) + " "
										+"("+ vals[per[1]] + " " + op(op1)
										+ " " + vals[per[2]] + "))" + " "
										+ op(op2) + " " + vals[per[3]] + ")");
								isset=true;
								break end;
							}
							if (solve(vals[per[0]]
									,solve(solve(vals[per[1]],vals[per[2]],op1),vals[per[3]],op2),op0)==10
									) {
								ln("(" + vals[per[0]] + " " + op(op0) + " "
										+"(("+ vals[per[1]] + " " + op(op1)
										+ " " + vals[per[2]] + ")" + " "
										+ op(op2) + " " + vals[per[3]] + "))");
								isset=true;
								break end;
							}
							if (solve(vals[per[0]]
									,solve(vals[per[1]],solve(vals[per[2]],vals[per[3]],op2),op1),op0)==10
									)  {
								ln("(" + vals[per[0]] + " " + op(op0) + " "
										+"(" + vals[per[1]] + " " + op(op1)
										+ " "+"(" + vals[per[2]] + " "
										+ op(op2) + " " + vals[per[3]] + ")))");
								isset=true;
								break end;
							}
							if (solve(solve(vals[per[0]],vals[per[1]],op0),solve(vals[per[2]],vals[per[3]],op2),op1)==10
									)  {
								ln("((" + vals[per[0]] + " " + op(op0) + " "
										+ vals[per[1]] +")"+ " " + op(op1)
										+ " "+"(" + vals[per[2]] + " "
										+ op(op2) + " " + vals[per[3]] + "))");
								isset=true;
								break end;
							}
				}
			}
			if(!isset){
				ln("0");
			}
		}
	}

	public static void main(String[] args) {
		new Main().run();
	}

	public static void pr(Object o) {
		System.out.print(o);
	}

	public static void ln(Object o) {
		System.out.println(o);
	}

	public static void ln() {
		System.out.println();
	}
}

class PermutationList implements Iterable<int[]> {
	private final int size;

	public PermutationList(int size) {
		if (size <= 0)
			throw new IllegalArgumentException();
		this.size = size;
	}

	public Iterator<int[]> iterator() {
		return new Iter(size);
	}

	private class Iter implements Iterator<int[]> {
		private final int[] source;
		private boolean isFirst = true;

		private Iter(int size) {
			source = new int[size];
			for (int i = 0; i < size; ++i) {
				source[i] = i;
			}
		}

		public boolean hasNext() {
			if (isFirst) {
				isFirst = false;
				return true;
			}

			int n = source.length;
			for (int i = n - 1; i > 0; i--) {
				if (source[i - 1] < source[i]) {
					int j = n;
					while (source[i - 1] >= source[--j])
						;
					swap(source, i - 1, j);
					reverse(source, i, n);
					return true;
				}
			}
			reverse(source, 0, n);
			return false;
		}

		public int[] next() {
			return source;
		}

		public void remove() {
			throw new UnsupportedOperationException();
		}

		private void swap(int[] is, int i, int j) {
			int t = is[i];
			is[i] = is[j];
			is[j] = t;
		}

		private void reverse(int[] is, int s, int t) {
			while (s < --t)
				swap(is, s++, t);
		}
	}
}