At IOI 2022, Team Canada encountered a mystery with the hotel elevators. Puzzled, they have asked you (their tour guide) to solve it for them.

The elevator system of the hotel can be viewed as a 2-D grid ~E~ with ~N~ floors and ~M~ elevators. The floors are numbered ~1~ to ~N~ from bottom to top and the elevators are numbered ~1~ to ~M~ from left to right. For each floor ~i~, ~E_{i,j}~ is ~1~ if elevator ~j~ stops at that floor and ~0~ if it doesn't. Each elevator can be used to travel between the floors it stops at.

A contiguous subsequence of floors ~[l, r]~ is defined as explorable if, starting from any floor in the subsequence, it is possible to reach all other floors in the subsequence while only entering floors numbered from ~l~ to ~r~.

Your task is to determine the length of the largest explorable contiguous subsequence of floors.

Constraints

~1 \le N \le 5 \times 10^4~

~1 \le M \le 500~

Subtask 1 [10%]

~1 \le N, M \le 300~

Subtask 2 [20%]

~1 \le M \le 10~

Subtask 3 [30%]

~1 \le M \le 50~

Subtask 4 [40%]

No additional constraints.

Input Specification

The first line contains ~2~ integers ~N~ and ~M~.

The next ~N~ lines each contain ~M~ characters (~0~ or ~1~), the ~j~-th character of the ~i~-th line representing ~E_{N-i+1,j}~.

Output Specification

Output the length of the largest explorable contiguous subsequence of floors.

Sample Input

5 3
001
010
011
100
001

Sample Output

3

Explanation for Sample

The largest contiguous subsequence of floors that is explorable is ~[3, 5]~.