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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <vector>
#include <map>
#include <set>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <queue>
#include <iomanip>
#include <list>
#include <string>

typedef char                SINT8;
typedef short               SINT16;
typedef int                 SINT32;
typedef long long           SINT64;
typedef double              DOUBLE;

#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))
#define rep(i,a,b) for(SINT64 (i)=SINT64(a);(i)<SINT64(b);(i)++)
#define rrep(i,a,b) for(SINT64 (i)=SINT64(a);(i)>=SINT64(b);(i)--)

#define put(a) cout << (a) << endl
#define puts(a) cout << (a) << " "


#define INF 1000000001
#define MOD 1000000007
#define INF64 1000000000000000001

#define F first
#define S second

#define Pii  pair<SINT32,SINT32>
#define Pll  pair<SINT64,SINT64>
#define Piii pair<SINT32,pair<SINT32,SINT32>>
#define Plll pair<SINT64,pair<SINT64,SINT64>>

#define Vll(a,b,c)    vector<vector<SINT64>> (a)((b),vector<SINT64>((c))
#define Vlll(a,b,c,d) vector<vector<vector<SINT64>>> (a)((b),vector<vector<SINT64>>((c),vector<SINT64>((d)))


using namespace std;

SINT64 N;
vector<vector<SINT64>> data(205,vector<SINT64>(205));

SINT64 dfs(SINT64 x, SINT64 d,vector<SINT64> g) {
	SINT64 buf = d;
	g[x] = 1;
	rep(i,0,N) {
		if ((data[x][i] == 1) && (g[i] == 0)) {
			buf = MAX(buf,dfs(i,d+1,g));
		}
	}
	return buf;
}

int main() {

	cin >> N;
	
	
	
	rep(i,0,N) {
		string s;
		cin >> s;
		rep(j,0,N) {
			data[i][j] = s[j]-'0';
		}
	}
	vector<SINT64> ok(N,-1);
	ok[0] = 0;

	queue<SINT64> bufq;
	bufq.push(0);
	while (bufq.size() != 0) {
		SINT64 buf = bufq.front();
		bufq.pop();
		rep(i,0,N) {
			if (data[buf][i] == 1) {
				if (ok[i] == -1) {
					ok[i] = 1 - ok[buf];
					bufq.push(i);
				} else if (ok[i] != 1 - ok[buf]) {
					put(-1);
					return 0;					
				}
			}
		}
	}



	SINT64 bans = 0;
	rep(c,0,N){
	queue<Pll> q;
	q.push(Pll(c,0));	
	vector<SINT64> ch(N,0);
	ch[0] = 1;
	while (q.size() != 0) {
		Pll buf = q.front();
		q.pop();
		rep(i,0,N) {
			if ((data[buf.F][i] == 1) && (ch[i] == 0)) {
				ch[i] = 1;
				q.push(Pll(i,buf.S+1));
				bans = MAX(bans,buf.S+1);
			}
		}
	}
	}
	
	

	put(bans+1);	
	return 0;
}


//	vector<vector<SINT64>> data(N,vector<SINT32>(3));										//2次元配列
//	vector<vector<vector<SINT64>>> data(N,vector<vector<SINT64>>(3,vector<SINT64>(3)));		//3次元配列

//	Vll(data,N,N);		//2次元配列
//	Vlll(data,N,N,N);	//3次元配列

//	sort(data.begin(),data.end());
//	sort(data.begin(),data.end(),std::greater<SINT64>());
//	__gcd(A,B);

//関数へのvectorポインタ渡し
//void dfs(SINT64 poi, SINT64 d, vector<vector<Pll>>& data) {
//}

/* 複数条件ソート
bool sortcompare(Pll A, Pll B) {
    if(A.F == B.F){
        return A.S > B.S;
    } else {
        return A.F < B.F;
    }
}

sort(data.begin(),data.end(),sortcompare);
*/

// タプル
//vector<tuple<SINT64,SINT64,SINT64>> edges;
//edges.emplace_back(a,b,c);
//cout << get<0>(edges[i]);
//cout << get<1>(edges[i]);
//cout << get<2>(edges[i]);
//sort(begin(edges), end(edges)); //ソート


//	data.emplace_back(BUF);			//後ろに追加

//  data.erase(std::unique(data.begin(), data.end()), data.end());	//ソート後に使用 同じ値を消す

//	data.insert(data.begin() + X, 0);	//X番目の要素に0を挿入


//	隣接リスト
//	vector<vector<SINT64>> data(N);
//	data[ A ].emplace_back( B );


// 両端キュー
//deque<SINT64> data;
//data.emplace_front(buf);	//先頭挿入


// lower_boundは値がなければ最大値(.size())を返す
// posi = lower_bound(data.begin(),data.end(), X) - data.begin();				// X以上を探す
// posi = lower_bound(data.begin(),data.end(),make_pair(X,0)) - data.begin();	//pair


/* 文字列回転
	string N;
	cin >> N;
	N = N[N.length()-1] + N.substr(0,N.length()-1);

	s = to_string(i);	//ストリング変換
*/
/* 文字列合成
	string N,M;
	cin >> N >> M;
	SINT64 ans = 0;
	ans = stoi(N+M);
*/

/*  文字列変更
	string s;	cin >> s;
	rep(i,0,s.length()) {	
		s[i] = (((s[i]-'A' + N) % 26) + 'A');
	}
	put(s);
*/

/*
//ワーシャルフロイド
	vector<vector<SINT64>> dist(N,vector<SINT64>(N,INF64));
	rep(i,0,N) {
		dist[i][i] = 0;
	}
	rep(k,0,N) {
		rep(i,0,N) {
			rep(j,0,N) {
				dist[i][j] = MIN(dist[i][j], dist[i][k]+dist[k][j]);
			}
		}
	}
*/

/*  優先度付きキュー
	priority_queue<SINT64, vector<SINT64>, greater<SINT64>> bufq;	//小さいほうから取り出せる
	priority_queue<SINT64, vector<SINT64>> bufq;					//大きいほうから取り出せる

	bufq.push(X);	//X を挿入
	bufq.top();		//先頭データ読み
	bufq.pop();		//先頭データ削除
*/

/* キュー
	queue<SINT64> bufq;	//宣言
	bufq.push(0);	//挿入
	bufq.front();	//先頭データ読み
	bufq.pop();		//先頭データ削除
*/





/* SET コンテナ
	set<SINT64> data;
	data.insert(X);				//X を挿入
	data.erase(data.begin());	//先頭を削除
	data.erase(--data.end());	//末尾を削除
	*data.begin();				//先頭要素にアクセス
	*data.rbegin();				//末尾要素にアクセス

	//全表示
    set<SINT64>::iterator it; //イテレータを用意
    for(it = data.begin(); it != data.end(); it++) {
        cout << *it << " ";
    }
	cout << endl;

	//N番目を一部表示
	set<SINT64>::iterator it; //  イテレータを用意
	it = data.begin();
	rep (i,0,N) {
		it++;
	}
	cout << *it << endl;
*/

/* map
	map<string,SINT32> mp;
	SINT32 N = 0;
	SINT32 mx = 0;

	cin >> N;
	for (SINT32 i = 0; i < N; i++) {
		string s;
		cin >> s;
		mp[s]++;
	}
	for(auto it=mp.begin();it!=mp.end();it++) {
		mx=max(mx,it->second);
	}

	//abc146E
	map<SINT64,SINT64> mp;
	rep(i,0,N+1) {
		ans += mp[rui[i]];
		mp[rui[i]]++;
		bufq.push(rui[i]);
		if (bufq.size() == M) {
			mp[bufq.front()]--;
			bufq.pop();
		}
	}
*/

/*
	//順列全表示
	//sortしてからでないと全列挙にならない
	sort(data.begin(),data.end());
	do {
		cout << buf << endl;
		rep(i,0,R) {
			cout << data[i] << " ";
		}
		cout << endl;

    } while (next_permutation(data.begin(),data.end()));
*/

/* bit数数え上げ
SINT64 bits64(SINT64 bits)
{
    bits = (bits & 0x55555555) + (bits >> 1 & 0x55555555);
    bits = (bits & 0x33333333) + (bits >> 2 & 0x33333333);
    bits = (bits & 0x0f0f0f0f) + (bits >> 4 & 0x0f0f0f0f);
    bits = (bits & 0x00ff00ff) + (bits >> 8 & 0x00ff00ff);
    return (bits & 0x0000ffff) + (bits >>16 & 0x0000ffff);
}
*/

//bitシフトのLONG対応
// ans += (1L<<50);



//  桁指定表示
//  ans = ans * M_PI;
//	cout << setprecision(15) << ans << endl;

// 桁数0埋め
// cout << std::setfill('0') << std::right << std::setw(2) << 5; //05


// 逆元　コンビネーション
/*
SINT64 modpow(SINT64 a, SINT64 p) {
	if (p == 0) return 1;
	if (p % 2 == 0) {
		//pが偶数の時
		SINT64 halfP = p / 2;
		SINT64 half = modpow(a, halfP);
		//a^(p/2) をhalfとして、half*halfを計算
		return half * half % MOD;
	} else {
		//pが奇数の時は、偶数にするために1減らす
		return a * modpow(a, p - 1) % MOD;
	}
}

SINT64 calcComb(SINT64 a, SINT64 b) {
	SINT64 Mul = 1;
	SINT64 Div = 1;
	SINT64 ans = 0;

	if (b > a - b) {
		return calcComb(a, a - b);
	}
 
	rep(i,0,b) {
		Mul *= (a - i);
		Div *= (i + 1);
		Mul %= MOD;
		Div %= MOD;
	}
	ans = Mul * modpow(Div, MOD - 2) % MOD;
	return ans;
}
*/


/* UNION FIND
class UnionFind {
public:
	vector<SINT64> parent;

	UnionFind(SINT64 N) {
		parent = vector<SINT64>(N+10, -1);	//少し多めに
	}
	
	SINT64 root(SINT64 A) {
		if (parent[A] < 0) {
			return A;
		} else {
			parent[A] = root(parent[A]);
			return parent[A];
		}
	}

	SINT64 size(SINT64 A) {
		return parent[root(A)] * (-1);
	}

	bool judge(SINT64 A, SINT64 B) {
		A = root(A);
		B = root(B);
		if (A == B) {
			return true;	//同じグループ
		} else {
			return false;	//違うグループ
		}
	}

	void connect(SINT64 A, SINT64 B) {
		A = root(A);
		B = root(B);
		if (A != B) {
			if (size(A) < size(B)) {
				swap(A, B);
			}
			parent[A] += parent[B];
			parent[B] = A;
		}
	}
};
UnionFind uni(N);
 */

/*
class SegTree {
private:
	SINT64 size;
	vector<SINT64> node;

	SINT64 jugdement(SINT64 a, SINT64 b) {
		SINT64 ans = 0;
		ans = a+b;
		return ans;
	}

public:

	//コンストラクタ
	SegTree(vector<SINT64> data) {
		SINT64 ori_size;
		ori_size = data.size();
		size = 1;
		while (size < ori_size) {
			size *= 2;
		}
		node.resize(2*size-1, 0);

		rep(i,0,ori_size) {
			node[size-1+i] = data[i];
		}
		rrep(i,size-2,0) {
			node[i] = jugdement(node[2*i+1], node[2*i+2]);
		}
	}

	//データ更新
	void update(SINT64 x, SINT64 val) {
		x += (size - 1);
    	node[x] = val+node[x];
    	while(x > 0) {
        	x = (x - 1) / 2;
        	node[x] = jugdement(node[2*x+1], node[2*x+2]);
		}
	}

	//データ取得 [a,b)
	SINT64 getdata(SINT64 a, SINT64 b, SINT64 k = 0, SINT64 l = 0, SINT64 r = -1) {
		if (r < 0) {
			r = size;
		}

		//要求範囲外
		if ((r <= a) || (b <= l)) {
			return 0;
		}
		//完全要求区間内
		if ((a <= l) && (r <= b)) {
			return node[k];
		}

    	SINT64 vl = getdata(a, b, 2*k+1, l, (l+r)/2);
    	SINT64 vr = getdata(a, b, 2*k+2, (l+r)/2, r);
    	return jugdement(vl, vr);
	}

	//表示
	void disp() {
		rep(i,0,size) {
			puts(node[size-1+i]);
		} cout << endl;
	}

	void alldisp() {
		SINT64 cnt = 0;
		SINT64 end = 2;
		
		while (1) {
			puts(node[cnt]);
			if (cnt == end-2) {
				end *= 2;
				cout << endl;
			}
			cnt++;
			if (cnt == size*2-1) {
				break;
			}
		}	
	}
};

SegTree seg(N);
 */