*complete combustion* is! Not wanting to disappoint his teacher, who thinks could do better in the class if he tried, has decided to bother you into doing his homework.

The homework sheet involves balancing hundreds of complete combustion chemical equations. In his homework, only three types of atoms (elements) are involved:

- Carbon (represented by )
- Hydrogen (represented by )
- and Oxygen (represented by )

The general form of such an equation looks like this:

can be any combination of carbon, hydrogen, or oxygen.

In order for the chemical equation to be balanced, the number of atoms of each element (, , and ) must be equal on both sides of the arrow, since atoms cannot be created or destroyed during the reaction. This can be done by setting , , , and to some positive integer value, signifying the number of copies of the substance. A subscript in front of an element signifies the amount of that element in the substance. In the input and output, a subscript will simply be an integer after an element. If there is no subscript in front of an element, there is only one of it.

For example, (`2CH3OH`

in input/output format) contains 2 carbon atoms, 8 hydrogen atoms, and 2 oxygen atoms.

Can you help

finish his homework?#### Input Specification

The first and only line of input will contain a single string, . It is guaranteed that will not begin with a number and will only contain numbers, `C`

, `H`

, and `O`

.

The total amount of each element in will not be greater than .

#### Output Specification

On a single line, output the balanced chemical equation in the form of `aR + bO2 -> cCO2 + dH2O`

, where , , , and are in lowest terms and cause the equation to be balanced, and is the exact copy of what was given in the input.

If it is not possible to balance the equation, simply output `Impossible`

.

#### Sample Input 1

`CH3CH2CH3`

#### Sample Output 1

`1CH3CH2CH3 + 5O2 -> 3CO2 + 4H2O`

#### Sample Input 2

`CH3OH`

#### Sample Output 2

`2CH3OH + 3O2 -> 2CO2 + 4H2O`

#### Sample Input 3

`H2O`

#### Sample Output 3

`Impossible`

## Comments

This might be my favourite question yet

no

can you use 0 of an element?

"a, b, c, and d to some positive integer value"

you say R cannot begin with a number yet you say 2CH3OH in the sample input

2CH3OH is not in any sample input.

A little wrong in this problem and I don't have enough time to solve problem P4, P5 and P6. So sad :(

On a single line, output the balanced chemical equation in the form of aR + bO2 -> cCO2 + dH2O, where aa, bb, cc, and dd are in lowest terms and cause the equation to be balanced, and RR is the exact copy of what was given in the input. For example, 2CH3OH2CH3OH (2CH3OH in

input/output) contains 2 carbon atoms, 8 hydrogen atoms, and 2 oxygen atoms. If R is 2CH3OH then how to print output?It is guaranteed that R will not begin with a number.

Can R is CH3(CH2)3(OH)6 ???

No, there are no brackets in R.