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B - Graph Partition /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

N 頂点 M 辺の連結無向グラフが与えられます。頂点には 1 から N までの番号がついています。 辺の情報はマス目 S を用いて表され、S_{i,j}1 のとき頂点 i,j を結ぶ辺が存在し、そうでないとき存在しないことを表します。

• どの辺も、番号が隣り合う頂点集合の頂点どうしを結ぶ。より正確には、どの辺 (i,j) に対しても、ある 1\leq t\leq k-1 が存在し、i\in V_t,j\in V_{t+1} または i\in V_{t+1},j\in V_t のいずれかを満たす。

### 制約

• 2 \leq N \leq 200
• S_{i,j}0 または 1 である
• S_{i,i}0 である
• S_{i,j}=S_{j,i}
• 与えられるグラフは連結
• N は整数である

### 入力

N
S_{1,1}...S_{1,N}
:
S_{N,1}...S_{N,N}


### 入力例 1

2
01
10


### 出力例 1

2


### 入力例 2

3
011
101
110


### 出力例 2

-1


### 入力例 3

6
010110
101001
010100
101000
100000
010000


### 出力例 3

4


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