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 $[3,5]$.