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.util.*;
import java.math.*;

public class B implements Runnable {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer st;
	static Random rnd;

	private void solve() throws IOException {
		int n = nextInt(), k = nextInt();
		int[][] digits = new int[n][k];
		for (int i = 0; i < n; i++) {
			String s = nextToken();
			for (int j = 0; j < k; j++) {
				digits[i][j] = (s.charAt(j) - '0');
			}
		}
		int result = rec(0, k, n, digits, new int[k], new boolean[k]);
		out.println(result);
	}

	private int rec(int step, int k, int n, int[][] digits, int[] history,
			boolean[] used) {
		if (step == k) {
			return check(k, n, digits, history);
		} else {
			int result = Integer.MAX_VALUE;
			for (int i = 0; i < k; i++) {
				if (!used[i]) {
					used[i] = true;
					history[step] = i;
					result = Math.min(result,
							rec(step + 1, k, n, digits, history, used));
					used[i] = false;
				}
			}
			return result;
		}
	}

	private int check(int k, int n, int[][] digits, int[] history) {
		int max = Integer.MIN_VALUE, min = Integer.MAX_VALUE;
		for (int i = 0; i < n; i++) {
			int current = 0;
			for (int j = 0; j < k; j++) {
				current = 10 * current + digits[i][history[j]];
			}
			max = Math.max(max, current);
			min = Math.min(min, current);
		}
		return max - min;
	}

	public static void main(String[] args) {
		new B().run();
	}

	public void run() {
		try {
			final String className = this.getClass().getName().toLowerCase();

			try {
				in = new BufferedReader(new FileReader(className + ".in"));
				out = new PrintWriter(new FileWriter(className + ".out"));
				// in = new BufferedReader(new FileReader("input.txt"));
				// out = new PrintWriter(new FileWriter("output.txt"));
			} catch (FileNotFoundException e) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			}

			rnd = new Random();

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	private String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = in.readLine();

			if (line == null)
				return null;

			st = new StringTokenizer(line);
		}

		return st.nextToken();
	}

	private int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	private long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	private double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}