Problem E. Equation

Author:ACM ICPC 2007-2008, Northeastern European Regional Contest   Time limit:3 sec
Input file:equation.in   Memory limit:64 Mb
Output file:equation.out  

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:

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:

Sample tests

No. Input file (equation.in) Output file (equation.out)
1
4 X * 2 + 2 /
X = -1/2
2
2 2 *
NONE
3
0 2 X / *
MULTIPLE

0.086s 0.011s 13