You are given a bunch of wooden sticks. Each endpoint of each stick is colored with some color. Is it possible to align the sticks in a straight line such that the colors of the endpoints that touch are of the same color?

Input

Input is a sequence of lines, each line contains two words, separated by spaces, giving the colors of the endpoints of one stick. A word is a sequence of lowercase letters no longer than 10 characters. There is no more than 250000 sticks.

Output

If the sticks can be aligned in the desired way, output a single line saying Possible, otherwise output Impossible.


There are multiple test cases in the input. There is a blank line between each test case.
Sample Input

blue red
red violet
cyan blue
blue magenta
magenta cyan

blue red
red violet
cyan blue
blue magenta
magenta cyan

Sample Output

Possible
Possible

Hint

Huge input,scanf is recommended.

Source

The UofA Local 2000.10.14