Score : $500$ points

Problem Statement

Given is a connected undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ to $N$, and the edges are described by a grid of characters $S$. If $S_{i,j}$ is 1, there is an edge connecting Vertex $i$ and $j$; otherwise, there is no such edge.

Determine whether it is possible to divide the vertices into non-empty sets $V_1, \dots, V_k$ such that the following condition is satisfied. If the answer is yes, find the maximum possible number of sets, $k$, in such a division.

• Every edge connects two vertices belonging to two "adjacent" sets. More formally, for every edge $(i,j)$, there exists $1\leq t\leq k-1$ such that $i\in V_t,j\in V_{t+1}$ or $i\in V_{t+1},j\in V_t$ holds.

Constraints

• $2 \leq N \leq 200$
• $S_{i,j}$ is 0 or 1.
• $S_{i,i}$ is 0.
• $S_{i,j}=S_{j,i}$
• The given graph is connected.
• $N$ is an integer.

Input

Input is given from Standard Input in the following format:

$N$

$S_{1,1}...S_{1,N}$

$:$

$S_{N,1}...S_{N,N}$

Output

If it is impossible to divide the vertices into sets so that the condition is satisfied, print $-1$. Otherwise, print the maximum possible number of sets, $k$, in a division that satisfies the condition.

2
01
10

2

We can put Vertex $1$ in $V_1$ and Vertex $2$ in $V_2$.

3
011
101
110

-1

6
010110
101001
010100
101000
100000
010000

4