M. Forgotten Spell
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Three mages are trying to remember a spell. Each of them believes the spell is some string of length n and it is known that each of the mages is mistaken in at most one letter. It is required to restore the forgotten spell.

Input

Three strings of the same length n (1 ≤ n ≤ 200000) are given in the input. They consist of lowercase Latin letters.

Output

If such a situation is not possible, output «Impossible».

If there are several spells satisfying the conditions, output «Ambiguous».

Finally, if the forgotten spell is the only one possible, output it.

Examples
Input
aab
aca
daa
Output
aaa
Input
abc
aca
abc
Output
Ambiguous
Input
abcde
fghij
klmno
Output
Impossible