Codeforces Round 290 (Div. 2) |
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C. Fox And Names

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFox Ciel is going to publish a paper on FOCS (Foxes Operated Computer Systems, pronounce: "Fox"). She heard a rumor: the authors list on the paper is always sorted in the lexicographical order.

After checking some examples, she found out that sometimes it wasn't true. On some papers authors' names weren't sorted in lexicographical order in normal sense. But it was always true that after some modification of the order of letters in alphabet, the order of authors becomes lexicographical!

She wants to know, if there exists an order of letters in Latin alphabet such that the names on the paper she is submitting are following in the lexicographical order. If so, you should find out any such order.

Lexicographical order is defined in following way. When we compare *s* and *t*, first we find the leftmost position with differing characters: *s*_{i} ≠ *t*_{i}. If there is no such position (i. e. *s* is a prefix of *t* or vice versa) the shortest string is less. Otherwise, we compare characters *s*_{i} and *t*_{i} according to their order in alphabet.

Input

The first line contains an integer *n* (1 ≤ *n* ≤ 100): number of names.

Each of the following *n* lines contain one string *name*_{i} (1 ≤ |*name*_{i}| ≤ 100), the *i*-th name. Each name contains only lowercase Latin letters. All names are different.

Output

If there exists such order of letters that the given names are sorted lexicographically, output any such order as a permutation of characters 'a'–'z' (i. e. first output the first letter of the modified alphabet, then the second, and so on).

Otherwise output a single word "Impossible" (without quotes).

Examples

Input

3

rivest

shamir

adleman

Output

bcdefghijklmnopqrsatuvwxyz

Input

10

tourist

petr

wjmzbmr

yeputons

vepifanov

scottwu

oooooooooooooooo

subscriber

rowdark

tankengineer

Output

Impossible

Input

10

petr

egor

endagorion

feferivan

ilovetanyaromanova

kostka

dmitriyh

maratsnowbear

bredorjaguarturnik

cgyforever

Output

aghjlnopefikdmbcqrstuvwxyz

Input

7

car

care

careful

carefully

becarefuldontforgetsomething

otherwiseyouwillbehacked

goodluck

Output

acbdefhijklmnogpqrstuvwxyz

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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