A firmware event log records n status codes (non-negative integers). Two codes are placed in the same group if and only if they have the same Hamming weight (the number of 1 bits in their binary representation).
Given the log, report the size of the largest such group.
Input format
Line 1: an integer n.
Line 2: n space-separated non-negative integers, the status codes.
Output format
A single integer: the number of codes in the largest Hamming-weight group.
Constraints
- 1 ≤ n ≤ 2000
- 0 ≤ status code ≤ 1,000,000,000