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.io.*;
public class a {
public static void main(String[] args) throws IOException
{
    input.init(System.in);
    PrintWriter out = new PrintWriter(System.out);
    int n = input.nextInt(), k = input.nextInt();
    data = new ArrayList<String>();
    for(int i =0; i<n; i++) data.add(input.next());
    out.println(go(new int[k], new boolean[k], 0));
    out.close();
}
static ArrayList<String> data;
static int go(int[] numbers, boolean[] used, int at)
{
    int n = numbers.length;
    if(at == n)
    {
        //process
        //System.out.println(Arrays.toString(numbers));
        int[] nums = new int[data.size()];
        int cur = 0;
        for(int i = 0; i<data.size(); i++)
        {
            String s = "";
            for(int j= 0; j<n;j++) s += data.get(i).charAt(numbers[j]);
            nums[cur++] = Integer.parseInt(s);
        }
        Arrays.sort(nums);
        return nums[nums.length-1] - nums[0];
    }
    int res = 987654321;
    for(int i = 0; i<n; i++)
    {
        if(!used[i])
        {
            used[i] = true;
            numbers[at] = i;
            res = Math.min(res, go(numbers, used, at+1));
            used[i] = false;
        }
    }
    return res;
}
static int gcd(int a, int b)
{
    if(b==0) return a;
    return gcd(b, a%b);
}
static class Soldier implements Comparable<Soldier> {
    int b, i;
    public Soldier(int bb, int ii)
    {
        b = bb; i = ii;
    }
    @Override
    public int compareTo(Soldier that) {
        // TODO Auto-generated method stub
        return that.b - this.b;
    }
}
public static class input {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
    static long nextLong() throws IOException {
        return Long.parseLong( next() );
    }
}
static class IT
{
    int[] left,right, val, a, b;
    IT(int n)
    {
        left = new int[4*n];
        right = new int[4*n];
        val = new int[4*n];
        a = new int[4*n];
        b = new int[4*n];
        init(0,0, n);
    }
    int init(int at, int l, int r)
    {
        a[at] = l;
        b[at] = r;
        if(l==r)
            left[at] = right [at] = -1;
        else 
        {
            int mid = (l+r)/2;
            left[at] = init(2*at+1,l,mid);
            right[at] = init(2*at+2,mid+1,r);
        }
        return at++;
    }
    //return the sum over [x,y]
    int get(int x, int y)
    {
        return go(x,y, 0);
    }
    int go(int x,int y, int at)
    {
        if(at==-1) return 0;
        if(x <= a[at] && y>= b[at]) return val[at];
        if(y<a[at] || x>b[at]) return 0;
        return go(x, y, left[at]) + go(x, y, right[at]);
    }
    //add v to elements x through y
    void add(int x, int y, int v)
    {
        go3(x, y, v, 0);
    }
    void go3(int x, int y, int v, int at)
    {
        if(at==-1) return;
        if(y < a[at] || x > b[at]) return;
        val[at] += (Math.min(b[at], y) - Math.max(a[at], x) + 1)*v;
        go3(x, y, v, left[at]);
        go3(x, y, v, right[at]);
    }
}
}