You are given an array A of length N. The partial digit subsequence of an array A is a subsequence of integers in which each consecutive integers have at least 1 digit in common. You are required to find the length of longest partial digit subsequence from the given array.

Input : 

• The first line of input contains N, length of array A.
• The second line of input contains N space-separated integers representing elements of A.

Output :

• Print an integer representing the maximum length of the longest partial digit subsequence of the given array A.

Constraints :

• \(1 \le N \le 10^{5}\)
• \(1 \le A_{i} \le 10^{18}\)