Algorithm

C. Fox And Names
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Fox 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: si ≠ ti. 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 si and ti 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 namei (1 ≤ |namei| ≤ 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
Copy
`3rivestshamiradleman`
output
Copy
`bcdefghijklmnopqrsatuvwxyz`
input
Copy
`10touristpetrwjmzbmryeputonsvepifanovscottwuoooooooooooooooosubscriberrowdarktankengineer`
output
Copy
`Impossible`
input
Copy
`10petregorendagorionfeferivanilovetanyaromanovakostkadmitriyhmaratsnowbearbredorjaguarturnikcgyforever`
output
Copy
`aghjlnopefikdmbcqrstuvwxyz`
input
Copy
`7carcarecarefulcarefullybecarefuldontforgetsomethingotherwiseyouwillbehackedgoodluck`
output
Copy
`acbdefhijklmnogpqrstuvwxyz`

Code Examples

#1 Code Example with C++ Programming

```Code - C++ Programming```

``````#include <iostream>
#include <vector>
#include <queue>
#include <string>
#include <algorithm>

using namespace std;

int in[26];
vector<int> g[26];
queue<int> q;
string s[100];

int main() {
int n, x, y;
cin >> n;

for (int i = 0; i < n; i++) cin >> s[i];

for (int i = 0; i + 1 < n; i++) {
int mn = min(s[i].length(), s[i + 1].length());

x = -1;
y = -1;
for (int j = 0; j < mn; j++)
if (s[i][j] != s[i + 1][j]) {
x = s[i][j];
y = s[i + 1][j];
break;
}

if (x == -1) {
if (s[i].length() > s[i + 1].length()) {
cout << "Impossible" << endl;
return 0;
}

continue;
}

x -= 'a';
y -= 'a';

g[x].push_back(y);
in[y]++;
}

for (int i = 0; i < 26; i++)
if (in[i] == 0)
q.push(i);

string res = "";

while (!q.empty()) {
int fr = q.front();
q.pop();
res += char(fr + 'a');

for (int i = 0; i < g[fr].size(); i++)
if (--in[g[fr][i]] == 0)
q.push(g[fr][i]);
}

if(res.length() == 26)
cout << res << endl;
else
cout << "Impossible" << endl;

return 0;
}``````
Copy The Code &

Input

cmd
3
rivest
shamir