Description

One cumbersome problem in chemistry is the task of making the number of atoms balanced in a chemical equation. Our problem is concerned with this.

Chemists obey these rules when they present chemical equations:

1. Each element name is abbreviated by at most two letters. The first letter is always in upper-case and the second letter if exists, is a lower-case letter (e.g. Calcium is represented by Ca, Oxygen by O, and Chlorine by Cl).

This means two molecules of chlorohydric acid (HCl) with one molecule of Calcium Hydroxide results in one molecule of Calcium Chloride (CaCl2) and two molecules of water.

Your task is to write a program to find appropriate coefficients x1 , x2 , …, xM and y1 , y2 , …, yN to balance an (imbalanced) equation like

in the following way:

Input

The first line contains an integer t (1 <= t <= 10), the number of test cases. Each test case consists of a single line containing an expression like:

Each Ai or Bi is a formula of a molecule according to the rules given in items 1 and 2.

The input equations are given in a way that if they can be balanced, xi and yi coefficients can be in the range of 1 to 9. There are less than 10 molecules and there are less than 10 different types of atoms, in a given equation. Additionally, you may assume molecules contain no more than 3 different kinds of atoms. You may also assume that there is no blank character in the input file, and the maximum length of the input lines is 200 characters.

Output

The output will be one line per test case containing the list of required coefficients, separated by blank characters, in the following order:

The coefficients should be integers in the range of 1..9. Obviously, there may be more than one answer for a test case. In such situations, print the answer which minimizes the number:

(This is an (M+N)-digit decimal number whose digits are xi and yi coefficients.) If the equation is impossible to balance, the output line should be IMPOSSIBLE.

3
HCl+CaO2H2=CaCl2+H2O
HCl+H2SO4=NaCl
HCl+NaOH=NaCl+H2O

2 1 1 2
IMPOSSIBLE
1 1 1 1

Source

Tehran 2003