# A DP Problem

Time Limit: 1 Second Memory Limit: 32768 KB

In this problem, you are to solve a very easy linear equation with only one variable x with no parentheses! An example of such equations is like the following:

An expression in its general form, will contain a '=' character with two expressions on its sides. Each expression is made up of one or more terms combined by '+' or '-' operators. No unary plus or minus operators are allowed in the expressions. Each term is either a single integer, or an integer followed by the lower-case character x or the single character x which is equivalent to 1x.

You are to write a program to find the value of x that satisfies the equation. Note that it is possible for the equation to have no solution or have infinitely many. Your program must detect these cases too.

## Input

The first number in the input line, t (1 <= t <= 10) is the number of test cases, followed by t lines of length at most 255 each containing an equation. There is no blank character in the equations and the variable is always represented by the lower-case character x. The coefficients are integers in the range (0...1000) inclusive.

## Output

The output contains one line per test case containing the solution of the equation. If s is the solution to the equation, the output line should contain [s] (the floor of s, i.e., the largest integer number less than or equal to s). The output should be **IMPOSSIBLE** or **IDENTITY** if the equation has no solution or has infinite solutions, respectively. Note that the output is case-sensitive.

## Sample Input

2 2x-4+5x+300=98x x+2=2+x

## Sample Output

3 IDENTITYSubmit

Source: Asia 2003, Tehran (Iran)