Problem: While exploring the old caves, researchers found a book, or more precisely, a stash of mixed pages from a book. Luckily, all of the original pages are present and each page contains its number. Therefore, the researchers can reconstruct the book.

After taking a deeper look into the contents of these pages, linguists think that this may be some kind of dictionary. What's interesting is that this ancient civilization used an alphabet which is a subset of the English alphabet, however, the order of these letters in the alphabet is not like the one in the English language.

Given the contents of pages that researchers have found, your task is to reconstruct the alphabet of this ancient civilization using the provided pages from the dictionary.

Input

First-line contains two integers: n and k (1 ≤ n, k ≤ 10^3) — the number of pages that scientists have found and the number of words present at each page. Following n groups contain a line with a single integer p_i (0 ≤ n < 10^3) — the number of i-th page, as well as k lines, each line containing one of the strings (up to 100 characters) written on the page numbered p_i.

Output

Output a string representing the reconstructed alphabet of this ancient civilization. If the book found is not a dictionary, output "IMPOSSIBLE" without quotes. In case there are multiple solutions, output any of them.

Example

Input


3 3
2
b
b
bbac
0
a
aca
acba
1
ab
c
ccb


Output


acb

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        solve(in, out);
        out.close();
    }

    static String reverse(String s) {
        return (new StringBuilder(s)).reverse().toString();
    }

    static void sieveOfEratosthenes(int n, int factors[]) 
    { 
        factors[1]=1;
        for(int p = 2; p*p <=n; p++) 
        { 
            if(factors[p] == 0) 
            { 
                factors[p]=p;
                for(int i = p*p; i <= n; i += p) 
                    factors[i] = p; 
            } 
        } 
    }

    static void sort(int ar[]) {
        int n = ar.length;
        ArrayList<Integer> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static void sort1(long ar[]) {
        int n = ar.length;
        ArrayList<Long> a = new ArrayList<>();
        for (int i = 0; i < n; i++)
            a.add(ar[i]);
        Collections.sort(a);
        for (int i = 0; i < n; i++)
            ar[i] = a.get(i);
    }

    static long ncr(long n, long r, long mod) {
        if (r == 0)
            return 1;
        long val = ncr(n - 1, r - 1, mod);
        val = (n * val) % mod;
        val = (val * modInverse(r, mod)) % mod;
        return val;
    }

    public static void solve(InputReader sc, PrintWriter pw) {
        int i, j = 0;
        int t = 1;  
        // int t = sc.nextInt();
        u: while (t-- > 0) {
            int n = sc.nextInt();
            int k = sc.nextInt();
            Pair words[] = new Pair[n*k];
            for(i=0;i<n;i++){
                int page = sc.nextInt();
                for(j=0;j<k;j++){
                    words[i*k+j] = new Pair(page,j,sc.next());
                }
            }
            Arrays.sort(words);
            boolean pres[] = new boolean[26];
            for(i=0;i<n*k;i++){
                for(j=0;j<words[i].ch.length();j++){
                    pres[words[i].ch.charAt(j)-'a'] = true;
                }
            }
            HashSet<Integer> next[] = new HashSet[26];
            int indeg[] = new int[26];
            for(i=0;i<26;i++)
                next[i] = new HashSet<>();
            for(i=1;i<n*k;i++){
                String w1 = words[i-1].ch;
                String w2 = words[i].ch;
                for(j=0;j<Math.min(w1.length(),w2.length());j++){
                    if(w1.charAt(j)!=w2.charAt(j)){
                        char ch1 = w1.charAt(j);
                        char ch2 = w2.charAt(j);
                        next[ch1-97].add(ch2-97);
                        indeg[ch2-97]++;
                        break;
                    }
                }
                if(j==w2.length()&&w1.length()>j){
                    pw.println("IMPOSSIBLE");
                    continue u;
                }
            }
            int y = -1;
            int vis[] = new int[26];
            for(i=0;i<26;i++){
                if(!pres[i]||vis[i]==1)
                    continue;
                HashSet<Integer> set = new HashSet<>();
                boolean cycle = chkCycle(vis,next,i,set);
                if(cycle){
                    pw.println("IMPOSSIBLE");
                    continue u;
                }
            }
            vis = new int[26];
            Stack<Integer> order = new Stack<>();
            for(i=0;i<26;i++){
                if(pres[i]&&vis[i]==0){
                    fill(order,i,next,vis);
                }
            }
            String ans = "";
            while(order.size()>0){
                ans+= (char)(order.pop() + 97);
            }
            pw.println(ans);
        }
    }

    static void fill(Stack<Integer> order, int i, HashSet<Integer> next[], int vis[]){
        if(vis[i]==1)
            return;
        vis[i] = 1;
        for(int a:next[i]){
            fill(order,a,next,vis);
        }
        order.add(i);
    }

    static boolean chkCycle(int vis[], HashSet<Integer> next[], int i, HashSet<Integer> set){
        if(set.contains(i))
            return true;
        boolean cycle = false;
        if(vis[i]==1)
            return false;
        set.add(i);
        vis[i] = 1;
        for(int a:next[i]){
            cycle = (cycle | chkCycle(vis,next,a,set));
        }
        set.remove(i);
        return cycle;
    }

    static class Pair implements Comparable<Pair> {
        int a;
        int b;
        // int c;
        String ch;
        
        Pair(int a, int b, String ch) {
            this.a = a;
            this.b = b;
            this.ch = ch;
        }
 
        public int compareTo(Pair p) {
            if(a!=p.a)
                return a-p.a;
            return b-p.b;
        }
    }

    static boolean isPrime(long n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
        if (n % 2 == 0 || n % 3 == 0)
            return false;
        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }

    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    static long fast_pow(long base, long n, long M) {
        if (n == 0)
            return 1;
        if (n == 1)
            return base % M;
        long halfn = fast_pow(base, n / 2, M);
        if (n % 2 == 0)
            return (halfn * halfn) % M;
        else
            return (((halfn * halfn) % M) * base) % M;
    }

    static long modInverse(long n, long M) {
        return fast_pow(n, M - 2, M);
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }
    }
}