C - Fox And Names (字符串加拓扑排序)

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：找到相应新的字典序使得所给的字符是按新型字典序从小到大排的。

做法：找到相邻串第一个字符不同的位置，连一条有向边，然后跑一遍拓扑排序即可。

#include<bits/stdc++.h> using namespace std; const int N=120; char s[N][N]; int ma[30][30],du[30],n; vector<int>ans; bool topu() { for(int k=1;k<=26;k++) { int pos=-1; for(int i=0;i<26;i++) { if(du[i]==0) { pos=i; break; } } if(pos==-1) return 0; ans.push_back(pos); du[pos]=-1; for(int i=0;i<26;i++) if(ma[pos][i]) du[i]--; } return 1; } int main() { cin>>n; for(int i=1;i<=n;i++) scanf("%s",s[i]+1); bool flag=1; for(int i=2;i<=n;i++) { int l1=strlen(s[i-1]+1); int l2=strlen(s[i]+1); int j=1; for(;j<=min(l1,l2);j++) { int c1=s[i-1][j]-'a'; int c2=s[i][j]-'a'; if(c1!=c2) { if(ma[c1][c2]==0) { ma[c1][c2]=1; du[c2]++; } break; } } if(j==min(l1,l2)+1&&l1>l2) { flag=0; break; } } if(!flag) { printf("Impossible\n"); exit(0); } if(topu()) { for(int i=0;i<ans.size();i++) printf("%c",ans[i]+'a'); } else printf("Impossible\n"); }