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Noonerized Spumbers

Time limit1sMemory limit1024 MB

Summary
Given a false arithmetic equation x op y = z, swap proper prefixes of two of the three numbers to make the equation true.
Level

Medium5 of 10

Topics
Brute force, String, Implementation, Math
Solved
No attempts yet

Problem

Everyone has heard of spoonerisms, named after William Archibald Spooner, an Oxford professor who had a habit of swapping prefixes of words, often with comical results. "May I show you to your seat?" became "May I sew you to your sheet?" and "a crushing blow" became "a blushing crow."

Just imagine him as a student of arithmetic, occasionally swapping the prefixes of the numbers he was calculating with and then wondering why his equations never made any sense. For instance, when he writes:

what he really intended to write was:

(He swapped prefixes "99" and "669669" in the first and third numbers.) And when he writes:

what he really intended to write was:

(He swapped the prefix "7272" with the prefix "6868" in the first and second numbers.)

Grading homework from young Mr. Spooner is quite a challenge. Fleas pined a way to help!

Input

The input consists of a single line containing an expression of the form "x+y=zx + y = z" or "x\*y=zx \* y = z", where xx, yy, and zz are positive integers less than 2312^{31}. There will be single spaces surrounding the "++" and "\*\*" operators and the "==" sign. The expression will not be a mathematically correct equation.

Output

Output a mathematically correct equation consisting of the input line modified by swapping proper prefixes of two of the three numbers xx, yy, zz. (A proper prefix of a string ss is a prefix that is neither empty nor equal to ss.) Separate the numbers, operators, and the "==" sign with single spaces. All integers in the correct equation will be non-negative and less than 2312^{31}. There is guaranteed to be only one possible correct equation that can be formed by swapping proper prefixes.

Examples2

  1. Example 1

    Input
    92 + 2803 = 669495
    
    Expected output
    6692 + 2803 = 9495
    
  2. Example 2

    Input
    6891 * 723 = 4979753
    
    Expected output
    7291 * 683 = 4979753