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.

#1
4 X * 2 + 2 /
#2
2 2 *
#3
0 2 X / *

#1
X = -1/2
#2
NONE
#3
MULTIPLE

Source

Northeastern Europe 2007