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.

The input consists of several test cases.
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.
Process to the end of file.

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.