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
题解：输入n个字符串，其中各个字符串的单词都是由一个字母表里的字母按从小到大排列组成的，求这个字母表，如果不存在输出“Impossible”。
#include<stdio.h>
#include<string.h>
#include<algorithm>
using namespace std;
char s[110][110],c[50];
int f[50],book[50][50],len[110];
void topo()
{
int i,j,k,ans=0;
for(i=0; i<26; i++)
{
int flag=0;
for(j=0; j<26; j++)
{
if(!f[j])//这个字母最小
{
flag=1;
break;
}
}
if(flag==0)//没有可确定的字母
{
printf("Impossible\n");
return;
}
f[j]--;
c[ans++]=j+'a';
for(k=0; k<26; k++)
if(book[j][k])
f[k]--;
}
c[ans]=0;
printf("%s\n",c);
}
int main()
{
int n;
while(~scanf("%d",&n))
{
int i,j,k,flag=0;
memset(book,0,sizeof(book));
memset(f,0,sizeof(f));
for(i=0; i<n; i++)
{
scanf("%s",s[i]);
len[i]=strlen(s[i]);
}
for(i=0; i<n; i++)
{
for(j=i+1; j<n; j++)
{
int l1=len[i],l2=len[j];
int minn=min(l1,l2),ff=0;
for(k=0; k<minn; k++)
{
if(s[i][k]!=s[j][k])
{
ff=1;
if(book[s[i][k]-'a'][s[j][k]-'a']==0)
{
book[s[i][k]-'a'][s[j][k]-'a']=1;
f[s[j][k]-'a']++;
}
break;
}
}
if(ff==0)//较短的单词结束也没有出现过不同的字母，说明较短的单词在另一个单词的前面
{
if(k!=l1)
{
flag=1;
break;
}
}
}
if(flag)
{
printf("Impossible\n");
break;
}
}
if(flag==0)
topo();
}
return 0;
}