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

C. Fox And Names

time limit per test

memory limit per test

input

output

lexicographical

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!

lexicographical

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 tiaccording to their order in alphabet.

Input

n (1 ≤ n ≤ 100): number of names.

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).

Sample test(s)

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

#include<iostream>
#include<algorithm>
#include<stdio.h>
#include<string.h>
#include<stdlib.h>

using namespace std;

char a[101][101];
int map[31][31],p[31];
int num[31];
int n,m;

void TP()
{
    int kk = 0;
    for(int i=0; i<26; i++)
    {
        for(int j=0; j<26; j++)
        {
            if(num[j] == 0)
            {
                p[kk++] = j;
                num[j]--;
                for(int k=0; k<26; k++)
                {
                    if(map[j][k] == 1)
                    {
                        num[k]--;
                    }
                }
                break;
            }
        }
    }
    if(kk<26)
    {
        printf("Impossible\n");
    }
    else
    {
        for(int i=0; i<kk; i++)
        {
            printf("%c",p[i]+'a');
        }
        printf("\n");
    }
}

int main()
{
    while(scanf("%d",&n)!=EOF)
    {
        memset(p,0,sizeof(p));
        memset(map,0,sizeof(map));
        memset(num,0,sizeof(num));

        for(int i=0; i<n; i++)
        {
            scanf("%s",a[i]);
        }
        int x,y;
        int flag = 0;
        for(int i=1; i<n; i++)
        {
            int len1 = strlen(a[i-1]);
            int len2 = strlen(a[i]);
            if(len1 > len2)
            {
                for(int j=0; a[i-1][j]!='\0'; j++)
                {
                    if(j == len2)
                    {
                        flag = 1;
                        break;
                    }
                    if(a[i][j]!=a[i-1][j])
                    {
                        x = a[i-1][j] - 'a';
                        y = a[i][j] - 'a';
                        if(map[x][y] == 0)
                        {
                            map[x][y] = 1;
                            num[y]++;
                        }

                        break;
                    }
                }
            }
            else if(len1 < len2)
            {
                for(int j=0; a[i][j]!='\0'; j++)
                {
                    if(j == len1)
                    {
                        break;
                    }
                    if(a[i][j]!=a[i-1][j])
                    {
                        x = a[i-1][j] - 'a';
                        y = a[i][j] - 'a';
                        if(map[x][y] == 0)
                        {
                            map[x][y] = 1;
                            num[y]++;
                        }

                        break;
                    }
                }
            }
            else
            {
                for(int j=0; a[i][j]!='\0'; j++)
                {
                    if(j == len1)
                    {
                        break;
                    }
                    if(a[i][j]!=a[i-1][j])
                    {
                        x = a[i-1][j] - 'a';
                        y = a[i][j] - 'a';
                        if(map[x][y] == 0)
                        {
                            map[x][y] = 1;
                            num[y]++;
                        }

                        break;
                    }
                }
            }

        }
        if(flag == 1)
        {
            printf("Impossible\n");
            continue;
        }
        TP();
    }
    return 0;
}