Description

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:

 4 X * 2 + 2 / 

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

Input

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

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.

<table style="border-color: black; border-collapse: collapse;" border="1"><tbody><tr><th>#1</th><td>4 X * 2 + 2 /</td></tr><tr><th>#2</th><td>2 2 *</td></tr><tr><th>#3</th><td>0 2 X / *</td></tr></tbody></table>

<table style="border-color: black; border-collapse: collapse;" border="1"><tbody><tr><th>#1</th><td>X = -1/2</td></tr><tr><th>#2</th><td>NONE</td></tr><tr><th>#3</th><td>MULTIPLE</td></tr></tbody></table>

Source