Algorithms and Data Structures

Create an equation

There are 3 operations that we can perform:
  1. (+) Addition modulo m
  1. (-) Subtraction modulo m
  1. (*) Multiplication modulo m
Given 3 integers , you are asked to place those operations between the numbers in such a way that the result of the equation is equal to 0.
All the operations are performed in standard mathematical order (first multiplication, then addition and subtraction from left to right).

Input

The first line of the input contains a single integer m (1 ≤ m ≤ ).
The next line contains 3 space-separated integers ( ≤ ≤ ).

Output

The program should print the resulting equation. If it’s impossible to obtain such an equation, the program should print Impossible.

Examples

Input
Output
5 8 2 4
8 * 2 + 4
 

Constraints

Time limit: 2.4 seconds

Memory limit: 512 MB

Output limit: 1 MB

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