Problem: You are given n k-digit integers. You have to rearrange the digits in the integers so that the difference between the largest and the smallest number was minimum. Digits should be rearranged by the same rule in all integers.

Input

The first line contains integers n and k — the number and digit capacity of numbers correspondingly (1 ≤ n, k ≤ 8). Next n lines contain k-digit positive integers. Leading zeroes are allowed both in the initial integers and the integers resulting from the rearranging of digits.

Output

Print a single number: the minimally possible difference between the largest and the smallest number after the digits are rearranged in all integers by the same rule.

Examples

Input

6 4
5237
2753
7523
5723
5327
2537


Output

2700


Input

3 3
010
909
012


Output

3


Input

7 5
50808
36603
37198
44911
29994
42543
50156


Output

20522

Note

In the first sample, if we rearrange the digits in numbers as (3,1,4,2), then the 2-nd and the 4-th numbers will equal 5237 and 2537 correspondingly (they will be maximum and minimum for such order of digits).

In the second sample, if we swap the second digits and the first ones, we get integers 100, 99 and 102.

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;


 public class Main {
	private InputStream is;
	private PrintWriter out;
	int time = 0, dp[][], DP[][], start[], end[], val[], black[], MOD = (int)(1e9+7), arr[], arr1[];
	int MAX = 500010, N, K, p;
	ArrayList<Integer>[] amp, amp1;
	boolean b[], b1[];
	Pair prr[];
	char ch[][];
	HashSet<Integer> hs = new HashSet<>();

	public static void main(String[] args) throws Exception {
		new Thread(null, new Runnable() {
		public void run() {
			try {

		//new Main().soln();
		} catch (Exception e) {
				System.out.println(e);
			}
		}
	}, "1", 1 << 26).start();
		new Main().soln();
	}
	class Node{
		Node next;
		int value;
	}
	void solve() {
		N = ni(); K = ni();
		ch = new char[N][K];
		for(int i = 0; i<N; i++) ch[i] = ns().toCharArray();
		recur(0);
		System.out.println(ans);
		/*
		N = ni(); K= ni();
		arr = na(N);
		amp = (ArrayList<Integer>[]) new ArrayList[100000];
		p = 0;
		dp = new int[2000][2000];
		DP = new int[2000][2000];
		for(int i = 0;i<2000;i++) for (int j = 0; j< 2000;j++){
			DP[i][j] = -1;
			dp[i][j]=-1;
		}
		recur(0,0);
		//System.out.println(K);
		for(int i = 0; i< p ;i++){
			//System.out.println(amp[i]);
			arr1 = new int[amp[i].size()];
			N = arr1.length;
			for(int j = 0; j< N;j++){
				arr1[j] = amp[i].get(j);
			}
			recur1(0,0);
			//System.out.println(HS.size());
		}
		//System.out.println(HS);
		ArrayList<Integer> ans = new ArrayList<>();
		out.println(HS.size());
		
		for(int i : HS) ans.add(i);
		Collections.sort(ans);
		for(int i : ans) out.print(i+" ");*/
		
	}
	int ans = Integer.MAX_VALUE;
	ArrayList<Integer> bbb = new ArrayList<>();
	void recur(int i){
		if(i==K){
		//	System.out.println(bbb);
		StringBuilder sb = new StringBuilder();
		TreeSet<Integer> temp = new TreeSet<>();
		for(int j = 0; j<N;j++){
			sb = new StringBuilder();
			for(int k = 0; k<K;k++){
				sb.append(ch[j][bbb.get(k)]);
			}
			temp.add(Integer.parseInt(sb.toString()));
		}
		ans = Math.min(ans, (temp.last()-temp.first()));
		//System.out.println(ans);
		return;
		}
		for(int j = 0;j<K;j++){
			if(!bbb.contains(j)){
				bbb.add(j);
				recur(i+1);
				bbb.remove((Integer)(j));
			}
		}
	}
	HashSet<Integer> HS = new HashSet<>();
	void recur1(int n, int k){
		if(k>K) return;
		if(k<=K) HS.add(k);
		if(DP[n][k]!=-1) return;
		DP[n][k] = -1;
		for(int i = n; i<N;i++){
			recur1(i+1,k+arr[arr1[i]]);
		}
	}
	ArrayList<Integer> temp = new ArrayList<>();
	void recur(int n, int k){
		//System.out.println(k);
		//System.out.println(temp);
		if(k>K || n>=N) return;
		if(k==K){
			amp[p++] = (ArrayList<Integer>) temp.clone();
			return;
		}
		if(dp[n][k]!=-1) return;
		dp[n][k] = 1;
		for(int i = n; i< N; i++){
			temp.add(i);
			recur(i+1,k+arr[i]);
			temp.remove((Integer)i);
		}
	}
	int min(int x,int y){
		if(x<y) return x;
		return y;
	}
	int max(int x,int y){
		if(x>y) return x;
		return y;
	}
	void dfs(int x){
		b[x] = true;
		for(int i : amp[x]){
			if(!b[i]){
				dfs(i);
			}
		}
	}
	void buildGraph(int m){
		while(m-->0)
		{
			int x = ni(), y = ni();
			amp[--x].add(--y);
		}
	}
	long modInverse(long a, long mOD2){
        return  power(a, mOD2-2, mOD2);
	}
	long power(long x, long y, long m)
	{
		if (y == 0)
    return 1;
	long p = power(x, y/2, m) % m;
	p = (p * p) % m;

	return (y%2 == 0)? p : (x * p) % m;
	}
	boolean isPrime(int x){
		for(int i = 2;i*1L*i<=x;i++) if(x%i==0) return false;
		return true;
	}
	public long gcd(long a, long b){
		if(b==0) return a;
		return gcd(b,a%b);
	}
	void failFn(String str, int arr[]){
		int len = 0;
		arr[0] = 0;
		int i = 1;
		while(i<arr.length){
			if(str.charAt(i)==str.charAt(len)){
				arr[i++] = ++len;
				continue;
			}
			if(len == 0){
				arr[i] = len;
				i++;
				continue;
			}
			if(str.charAt(i)!=str.charAt(len)){
				len = arr[len-1];
			}
		}
	}
	static class ST1{
		int arr[], st[], size;
		ST1(int a[]){
			arr = a.clone();
			size = 10*arr.length;
			st = new int[size];
			build(0,arr.length-1,1);
		}
		void build(int ss, int se, int si){
			if(ss==se){
				st[si] = arr[ss];
				return;
			}
			int mid = (ss+se)/2;
			int val = 2*si;
			build(ss,mid,val); build(mid+1,se,val+1);
			st[si] = (st[val]+ st[val+1]);
		}
		int get(int ss, int se, int l, int r, int si){
			if(l>se || r<ss || l>r) return Integer.MAX_VALUE;
			if(l<=ss && r>=se) return st[si];
			int mid = (ss+se)/2;
			int val = 2*si;
			return (get(ss,mid,l,r,val)+ get(mid+1,se,l,r,val+1));
		}
	}
	static class ST{
		int arr[],lazy[],n;
		ST(int a){
			n = a;
			arr = new int[10*n];
			lazy = new int[10*n];
		}
		void up(int l,int r,int val){
			update(0,n-1,0,l,r,val);
		}
		void update(int l,int r,int c,int x,int y,int val){
			if(lazy[c]!=0){
				lazy[2*c+1]+=lazy[c];
				lazy[2*c+2]+=lazy[c];
				if(l==r)
					arr[c]+=lazy[c];
				lazy[c] = 0;
			}
			if(l>r||x>y||l>y||x>r)
				return;
			if(x<=l&&y>=r){
				lazy[c]+=val;
				return ;
			}
			int mid = l+r>>1;
			update(l,mid,2*c+1,x,y,val);
			update(mid+1,r,2*c+2,x,y,val);
			arr[c] = (arr[2*c+1]+ arr[2*c+2]);
		}
		int an(int ind){
			return ans(0,n-1,0,ind);
		}
		int ans(int l,int r,int c,int ind){
			if(lazy[c]!=0){
				lazy[2*c+1]+=lazy[c];
				lazy[2*c+2]+=lazy[c];
				if(l==r)
					arr[c]+=lazy[c];
				lazy[c] = 0;
			}
			if(l==r)
				return arr[c];
			int mid = l+r>>1;
			if(mid>=ind)
				return ans(l,mid,2*c+1,ind);
			return ans(mid+1,r,2*c+2,ind);
		}
	}
	public static class FenwickTree {
		
	    int[] array; // 1-indexed array, In this array We save cumulative information to perform efficient range queries and updates

	    public FenwickTree(int size) {
	        array = new int[size + 1];
	    }
	    public int rsq(int ind) {
	        assert ind > 0;
	        int sum = 0;
	        while (ind > 0) {
	            sum += array[ind];
	            //Extracting the portion up to the first significant one of the binary representation of 'ind' and decrementing ind by that number
	            ind -= ind & (-ind);
	        }
	        return sum;
	    }
	    public int rsq(int a, int b) {
	        assert b >= a && a > 0 && b > 0;
	        return rsq(b) - rsq(a - 1);
	    }
	    public void update(int ind, int value) {
	        assert ind > 0;
	        while (ind < array.length) {
	            array[ind] += value;
	            //Extracting the portion up to the first significant one of the binary representation of 'ind' and incrementing ind by that number
	            ind += ind & (-ind);
	        }
	    }
	    public int size() {
	        return array.length - 1;
	    }
	}
	public static int[] shuffle(int[] a, Random gen){
		for(int i = 0, n = a.length;i < n;i++)
		{ 
			int ind = gen.nextInt(n-i)+i; 
			int d = a[i]; 
			a[i] = a[ind];
			a[ind] = d; 
		} 
	return a; 
	}

	class Pair implements Comparable<Pair>{
		int u, v;
		Pair(int u, int v){
			this.u = u;
			this.v = v;
		}public int hashCode() {
			return Objects.hash();
		}
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return ((u == other.u && v == other.v));// || (v == other.u && u == other.v));
		}
		public int compareTo(Pair other) {
			//return Integer.compare(val, other.val);
			return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(other.v,v));
		}	
		public String toString() {
			return "[u=" + u + ", v=" + v + "]";
		}
	}
	long power(long x, long y, int mod){
		long ans = 1;
		while(y>0){
			if(y%2==0){
				x = (x*x)%mod;
				y/=2;
			}
			else{
				ans = (x*ans)%mod;
				y--;
			}
		}
		return ans;
	}
	void soln() {
		is = System.in;
		out = new PrintWriter(System.out);
		long s = System.currentTimeMillis();
		solve();
		//out.close();
		out.flush();
		//tr(System.currentTimeMillis() - s + "ms");
	}


	// To Get Input
	// Some Buffer Methods
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;

	private int readByte() {
		if (lenbuf == -1)
			throw new InputMismatchException();
		if (ptrbuf >= lenbuf) {
			ptrbuf = 0;
			try {
				lenbuf = is.read(inbuf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (lenbuf <= 0)
				return -1;
		}
		return inbuf[ptrbuf++];
	}

	private boolean isSpaceChar(int c) {
		return !(c >= 33 && c <= 126);
	}

	private int skip() {
		int b;
		while ((b = readByte()) != -1 && isSpaceChar(b))
			;
		return b;
	}

	private double nd() {
		return Double.parseDouble(ns());
	}

	private char nc() {
		return (char) skip();
	}
	private String ns() {
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
									// ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	private char[] ns(int n) {
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while (p < n && !(isSpaceChar(b))) {
			buf[p++] = (char) b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for (int i = 0; i < n; i++)
			map[i] = ns(m);
		return map;
	}

	private int[] na(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++)
			a[i] = ni();
		return a;
	}

	private int ni() {
		int num = 0, b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private long nl() {
		long num = 0;
		int b;
		boolean minus = false;
		while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
			;
		if (b == '-') {
			minus = true;
			b = readByte();
		}

		while (true) {
			if (b >= '0' && b <= '9') {
				num = num * 10 + (b - '0');
			} else {
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

	private void tr(Object... o) {
		if (!oj)
			System.out.println(Arrays.deepToString(o));
	}
}