Problem:
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.

Sample Input 1

2
01
10

Sample Output 1

2

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

Sample Input 2

3
011
101
110

Sample Output 2

-1

Sample Input 3

6
010110
101001
010100
101000
100000
010000

Sample Output 3

4

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

N = int(input())
S = []
for i in range(N):
    S.append(input())
    

#二部グラフ判定
L = [0 for i in range(N)]
L[0] = 1
q = [0]
res = 0

while len(q) > 0:
    idx = q.pop(-1)
    c = L[idx]*(-1)
    for i in range(N):
        if S[idx][i] == "1":
            if L[i] == 0:
                L[i] = c
                q.append(i)
            elif L[i] == c*(-1):
                res = 1
                q.clear()
                break
            

if res == 1:
    print(-1)
else:
    # Warshall-Floyd法で直径を求める
    d = [[10**4 for j in range(N)] for i in range(N)]
    # initialize
    for i in range(N):
        for j in range(N):
            if S[i][j] == "1":
                d[i][j] = 1
    
    # DP
    for k in range(N):
        for i in range(N):
            for j in range(N):
                if i != j:
                    d[i][j] = min(d[i][j], d[i][k]+d[k][j])

                
    ans = 0
    for i in range(N):
        for j in range(N):
            if d[i][j] < 10**4:
                ans = max(ans, d[i][j])
                
    print(ans+1)