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Задачи

708. Equation

Ограничения: время – 2s/4s, память – 64MiB Ввод: input.txt или стандартный ввод Вывод: output.txt или стандартный вывод copy
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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.

Sample input 1

4 X * 2 + 2 /

Sample output 1

X = -1/2

Sample input 2

2 2 *

Sample output 2

NONE

Sample input 3

0 2 X / *

Sample output 3

MULTIPLE

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