# Minimum Hamming Distance

Given

`n`

bit-strings, you are asked to find the pair of bit-strings that has the minimum hamming distance. Input

The first line of the input contains a single integer

`n`

(2 ≤ n ≤ 1000).The next

`n`

lines contain bit-strings of the same length each on a separate line (1 ≤ || ≤ ). Output

The program should print the minimum hamming distance of those pairs.

Examples

Input | Output |

4
1111
1010
0000
1011 | 1 |

Explanation

The hamming distance between

`1011`

and `1010`

is 1.#### Constraints

Time limit: 3 seconds

Memory limit: 512 MB

Output limit: 1 MB