Permutations

Description:

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.

Sample Input:

6 4
5237
2753
7523
5723
5327
2537

Sample Output:

2700

Sample Input:

3 3
010
909
012

Sample Output:

3

Sample Input:

7 5
50808
36603
37198
44911
29994
42543
50156

Sample 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.