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.util.*;
import java.lang.*;
import java.io.*;
import java.math.*;
import java.text.*;
public class Prac{     
    static class InputReader { 
        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        public InputReader(InputStream st) {
            this.stream = st;
        } 
        public int read() {
            if (snumChars == -1)
                throw new InputMismatchException();
            if (curChar >= snumChars) {
                curChar = 0;
                try {
                    snumChars = stream.read(buf);
                } 
                catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (snumChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }
        public int ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
            c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        } 
        public int[] nia(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        } 
        public String rs() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                    c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }
        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        } 
        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
 
        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        } 
    }
    public static class Key {

        private final int x;
        private final int y;

        public Key(int x, int y) {
            this.x = x;
            this.y = y;
        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (!(o instanceof Key)) return false;
            Key key = (Key) o;
            return x == key.x && y == key.y;
        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }

    }
    
    static PrintWriter w = new PrintWriter(System.out);
    static long mod=998244353L,mod1=1000000007;
    static int co[][];
    static void dsort(){
        Arrays.parallelSort(co,(o1,o2)->o1[0]!=o2[0]?o1[0]-o2[0]:o1[1]-o2[1]);
    }
     static long  power(long x, long y) { 
        long temp=0; 
        if( y == 0) 
            return 1; 
        temp = power(x, y/2); 
        if (y%2 == 0) 
            return (temp*temp)%mod1; 
        else
            return (((x*temp)%mod1)*temp)%mod1; 
    } 
    static long modInverse(long a, long m){
        long num=m;
        long x=1;
        long power=a%mod1;
        while(num>0){
              if(num%2==1){
                  x=(x*power)%mod1;
            }
            num>>=1;
            power=(power*power)%mod1;         
        }
        return x;
    }
    static long ncr(int n,int r){
        if(n<r)return 0L;
        long ans=fact[n]/(fact[r]*fact[n-r]);
        return ans;
    }
    static long fact[]=new long[1000005];
    public static void findFact(){
        fact[0]=1;
        for(int i=1;i<=1000000;i++){
            fact[i]=(i*fact[i-1])%mod1;
        }
    } 
    static long nCr(int n,int r){
        if(n<r)return 0L;
        
        return (fact[n]*modInverse((fact[r]*fact[n-r])%mod1,mod1-2))%mod1;
    }
    static Set<String> set = new HashSet<>(); 
  
    // Recursive function to generate 
    // permutations of the string 
    static void Permutation(String str, String ans) 
    { 
  
        // If string is empty 
        if (str.length() == 0) { 
  
            // Add the generated permutation to the 
            // set in order to avoid duplicates 
            set.add(ans); 
            return; 
        } 
  
        for (int i = 0; i < str.length(); i++) { 
  
            // ith character of str 
            char ch = str.charAt(i); 
  
            // Rest of the string after excluding 
            // the ith character 
            String ros = str.substring(0, i) 
                         + str.substring(i + 1); 
  
            // Recurvise call 
            Permutation(ros, ans + ch); 
        } 
    } 
    public static void main (String[] args)throws IOException{
        InputReader sc=new InputReader(System.in);
        //findFact();
        int n=sc.ni(),k=sc.ni();
        String p="";
        for(int i=1;i<=k;i++){
            p=p+Integer.toString(i);
        }
        Permutation(p,"");
        String s[]=new String[n];
        for(int i=0;i<n;i++){
            s[i]=sc.nextLine();
        }
        int ans=Integer.MAX_VALUE;
        for(String x:set){
            int min=Integer.MAX_VALUE,max=Integer.MIN_VALUE;
            for(int i=0;i<n;i++){
                String te="";
                for(int j=0;j<k;j++){
                    int in=x.charAt(j)-'1';
                    te=te+s[i].charAt(in);
                }
                int num=Integer.parseInt(te);
                min=Math.min(min,num);
                max=Math.max(max,num);
            }
            ans=Math.min(ans,max-min);
        }
        w.println(ans);
        w.close();
    }
}