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 Go (1.6) (judge verdict: Wrong Answer)

package main
import (
  "fmt"
  "container/list"
)
func main() {
  var n int
  var s string
  fmt.Scan(&n)
  g := make([][]int,n)
  for i:=0;i<n;i++ {
    fmt.Scan(&s)
    for j,r := range s {
      if r == '1' {
        g[i] = append(g[i],j)
        g[j] = append(g[j],i)
      }
    }
  }
  k := 0
  d := make([]int,n)
  for t:=0;t<2;t++ {
    for i:=0;i<n;i++ { d[i] = 0 }
    queue := list.New()
    d[k] = 1
    queue.PushBack(k)
    for queue.Len() > 0 {
      i,_ := queue.Remove(queue.Front()).(int)
      for _,j := range g[i] {
        if d[j] != 0 && d[j]%2 == d[i]%2 { fmt.Println(-1);return }
        if d[j] == 0 || d[j] > d[i]+1 {
          d[j] = d[i]+1
          queue.PushBack(j)
          continue
        }
      }
    }
    for i:=0;i<n;i++ {
      if d[k] < d[i] { k = i }
    }
  }
  fmt.Println(d[k])
}