C - 1-SAT

Score : $300$ points

Problem Statement

Given are $N$ strings $S_1, S_2, \dots, S_N$. Each of these is a non-empty string consisting of lowercase English letters, with zero or one ! added at the beginning.
We say a string $T$ to be unsatisfied when it matches one of $S_1, S_2, \dots, S_N$ regardless of whether we add an ! at the beginning of $T$.
Determine whether there exists an unsatisfied string. If so, present one such string.

Constraints

• $1 \le N \le 2 \times 10^5$
• $1 \le |S_i| \le 10$
• $S_i$ is a non-empty string consisting of lowercase English letters, with zero or one ! added at the beginning.

Input

Input is given from Standard Input in the following format:

$N$

$S_1$

$\vdots$

$S_N$

Output

If there exists an unsatisfied string, print one such string.
If there is no unsatisfied string, print satisfiable.

6
a
!a
b
!c
d
!d

a

a matches $S_1$ as is, and it matches $S_2$ when we add an !, so it is unsatisfied. Besides that, d will also be accepted.

10
red
red
red
!orange
yellow
!blue
cyan
!green
brown
!gray

satisfiable