Problem E. Equation ≡

Statement

Your task is to solve an equation of the form f(x) = 0 where f(x) is written in postfix notation with numbers, operations  + ,  − ,  * ,  / , and at most one occurrence of a variable x. For example, f(x) for an equation (4x + 2) / 2 = 0 is written as: 4X * 2 + 2 / 

The solution for f(x) = 0 is x =  − 1 / 2.

Input file format

The input file consists of a single line with at most 30 tokens separated by spaces.

Each token is either:

• a digit from 0 to 9;
• an operation  + ,  − ,  * , or  / ;
• an uppercase letter X that denotes variable x.

The input file contains a correct representation of f(x) in postfix notation where token X occurs at most once. There is no division by a constant zero in this equation, that is, there always exists a value of x, such that f(x) can be evaluated without division by zero.

Output file format

Write to the output file:

• X = p / q if equation f(x) = 0 has a single solution that can be represented with a simple fraction p / q, where p and q are coprime integer numbers and q is positive.
• NONE if equation f(x) = 0 has no solution;
• MULTIPLE if equation f(x) = 0 has multiple solutions.

Sample tests

4 X * 2 + 2 /

X = -1/2

2 2 *

NONE

0 2 X / *

MULTIPLE