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 PYTHON):

Solution:
#!/usr/bin/env python
# -*- coding: utf-8 -*-

import sys

def get_comb_operator(s, lim):
    lst = [""]
    next_lst = []
    for i in range(lim):
        next_lst = [ch + item for ch in s for item in lst]
        lst = next_lst
    return lst

def get_comb(lst):
    def sub(ans, comb, rest):
        if not rest:
            if not comb in ans:
                ans.append(comb)
        else:
            for i in range(len(rest)):
                sub(ans, comb + rest[i], rest[:i] + rest[i+1:])
    ans = []
    sub(ans, "", lst)
    return ans

def comb_all(nums, operators, expr = ""):
    if nums == "":
        yield expr + operators
    elif operators == "":
        yield expr + nums
    else:
        for item in comb_all(nums[1:], operators, expr + nums[0]):
            yield item
        for item in comb_all(nums, operators[1:], expr + operators[0]):
            yield item

def get_success_item(nums, operators):
    for expr in comb_all(nums, operators):
        if is_success(expr):
            return expr
    return ""

def is_success(expr):
    stack = []
    for i in xrange(len(expr)):
        if expr[i] in "*+-":
            if len(stack) < 2:
                return False
            else:
                first = stack.pop()
                second = stack.pop()
                if expr[i] == "*":
                    stack.append(second * first)
                elif expr[i] == "-":
                    stack.append(second - first)
                else:
                    stack.append(second + first)
        else:
            stack.append(int(expr[i]))
    return stack[0] == 10

def to_infix(expr):
    stack = []
    for i in xrange(7):
        if expr[i] in "+*-":
            first = stack.pop()
            second = stack.pop()
            stack.append("(%s %s %s)" % (second, expr[i], first))
        else:
            stack.append(expr[i])
    return stack[0]

def get_result(nums):
    for comb_num in get_comb(nums):
        for comb_operator in get_comb_operator("+*-", 3):
            success_item = get_success_item(comb_num, comb_operator)
            if success_item:
                return to_infix(success_item)
    return "0"

def solve():
    while True:
        comb_operator = get_comb_operator("+*-", 3)
        nums = sys.stdin.readline().strip().replace(" ", "")
        if nums != "0000":
            print get_result(nums)
        else:
            sys.exit()

if __name__ == "__main__":
    solve()