Equation

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: 4X2+2/ The solution for f(x) = 0 is x = −1/2. Input The input file consists of several equations, each of them in 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 For each test case, 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 4X2+2/ 22* 02X/* Sample Output X = -1/2 NONE MULTIPLE