Fox And Names CodeForces - 510C

问题：

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

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

题意：

按顺序给你一堆单词，单词只含小写字母，你需要改变字典序，使上面的单词按照你改后的字典序顺序排列。把你改变后的zi字典序输出来。

思路：

运用拓扑排序，靠前的单词要比靠后的单词第一个不相同的字母在字典序中的位置靠前，虽然看起来很难懂吧！然后就是如果靠后的单词与靠前的单词前面的序列完全相同，但是靠前的单词后面还有序列，这种情况一定找不出可行的字典序方案，需要特判一下。

代码：

#define N 1200
#include<stdio.h>
#include<string.h>
#include<algorithm>
char s[N][N];
int k[N];
int book[30][30];
void topolo()
{
    int d=0,i,j,flag,c[N];
    for(i=0; i<26; i++)
    {
        flag=0;
        for(j=0; j<26; j++)
        {
            if(k[j]==0)
            {
                flag=1;
                break;
            }
        }
        if(flag==0)
        {
            printf("Impossible\n");
            return;
        }
        k[j]=-1;
        c[d++]=j;
        for(int h=0; h<26; h++)
        {
            if(book[j][h]==1)
                k[h]--;
        }
    }
    for(i=0; i<26; i++)
        printf("%c",c[i]+'a');
    printf("\n");
}
int main()
{
    int n;

    while(~scanf("%d",&n))
    {
        for(int i=0; i<n; i++)
            scanf("%s",s[i]);
        int flag=0;
        memset(book,0,sizeof(book));
        memset(k,0,sizeof(k));
        for(int i=0; i<n; i++)
        {
            for(int j=i+1; j<n; j++)
            {
                int t=0,d;
                for(d=0; s[i][d]!='\0'&&s[j][d]!='\0'; d++)
                    if(s[i][d]!=s[j][d])//两序列第一个不相同的字母
                    {
                        t=1;
                        if(!book[s[i][d]-'a'][s[j][d]-'a'])
                        {
                            book[s[i][d]-'a'][s[j][d]-'a']=1;
                            k[s[j][d]-'a']++;
                        }
                        break;
                    }
                if(!t)//特判
                    if(s[i][d]!='\0')
                    {
                        flag=1;
                        break;
                    }
                if(flag)break;
            }
        }
        if(flag)
            printf("Impossible\n");
        else
            topolo();
    }
    return 0;
}