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 (GCC 5.4.1) (judge verdict: Accepted)

#if 0
cat <<EOF >mistaken-paste
#endif
// thx Ebi-chan!

// #pragma GCC optimize("unroll-loops")
// #pragma GCC optimize("O3")

#pragma GCC diagnostic ignored "-Wincompatible-pointer-types"
#define _USE_MATH_DEFINES

#include <stdio.h>
#include <stdint.h>
#include <stdlib.h>
#include <string.h>
#include <stdbool.h>
#include <math.h>
#include <time.h>

#define BIG 2000000007LL
#define VERYBIG 20000000000000007LL
#define ULTRABIG 3000000000000000000LL

#define MOD 1000000007LL
#define FOD  998244353LL
typedef uint64_t ull;
typedef  int64_t sll;

#define N_MAX 1048576

#ifdef __cplusplus
#include <queue>
#include <stack>
#include <tuple>
#include <set>
#include <map>
#include <string>
#include <algorithm>
#include <functional>
#include <array>

using std::queue;
using std::priority_queue;
using std::stack;
using std::tuple;
using std::set;
using std::map;
using std::vector;
using std::greater;
using std::pair;
using std::string;
using std::get;

template <typename T, typename U>
pair<T, U> operator+(pair<T, U> l, pair<T, U> r) {
	return pair<T, U>(l.first + r.first, l.second + r.second);
}

#endif

#ifndef M_PI
#define M_PI 3.14159265358979323846264338327950
#endif

typedef struct {
	sll a;
	sll b;
} hwll;

typedef struct {
	sll a;
	sll b;
	sll c;
} hwllc;

typedef struct {
	hwll a;
	hwll b;
} linell;

typedef struct {
	double a;
	double b;
} hwreal;

sll n, m;
sll h, w;
sll k;
sll q;
sll va, vb, vc, vd, ve, vf;
ull ua, ub, uc, ud, ue, uf;
long double vra, vrb, vrc;
double vda, vdb, vdc;
char ch, dh;

ull umin (ull x, ull y) {
	return (x < y) ? x : y;
}

ull umax (ull x, ull y) {
	return (x > y) ? x : y;
}

sll smin (sll x, sll y) {
	return (x < y) ? x : y;
}

sll smax (sll x, sll y) {
	return (x > y) ? x : y;
}

double dmin (double x, double y) {
	return (x < y) ? x : y;
}

double dmax (double x, double y) {
	return (x > y) ? x : y;
}

ull gcd (ull x, ull y) {
	if (y == 0) {
		return x;
	} else {
		return gcd(y, x % y);
	}
}

ull bitpow (ull a, ull x, ull modulo) {
	ull result = 1;
	while (x) {
		if (x & 1) {
			result *= a;
			result %= modulo;
		}
		x /= 2;
		a = (a * a) % modulo;
	}
	return result;
}

ull divide (ull a, ull b, ull modulo) {
	return (a * bitpow(b, modulo - 2, modulo)) % modulo;
}

ull udiff (ull a, ull b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

sll sdiff (sll a, sll b) {
	if (a >= b) {
		return a - b;
	} else {
		return b - a;
	}
}

int bitcount (ull n) {
	int result = 0;
	while (n) {
		if (n & 1) result++;
		n /= 2;
	}
	return result;
}

#define BEGCMP(NAME) int32_t NAME (const void *left, const void *right)
#define DEFLR(TYPE) TYPE l=*(TYPE*)left,r=*(TYPE*)right
#define CMPRET(L, R) if((L)<(R))return-1;if((L)>(R))return+1

// int32_t pullcomp (const void *left, const void *right) {
// 	ull l = *(ull*)left;
// 	ull r = *(ull*)right;
// 	if (l < r) {
// 		return -1;
// 	}
// 	if (l > r) {
// 		return +1;
// 	}
// 	return 0;
// }
BEGCMP(pullcomp){
	DEFLR(ull);
	CMPRET(l, r);
	return 0;
}
BEGCMP(prevcomp){
	DEFLR(sll);
	CMPRET(r, l);
	return 0;
}
BEGCMP(psllcomp){
	DEFLR(sll);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pcharcomp){
	DEFLR(char);
	CMPRET(l, r);
	return 0;
}
BEGCMP(pdoublecomp){
	DEFLR(double);
	CMPRET(l, r);
	return 0;
}

int32_t pstrcomp (const void *left, const void *right) {
	char* l = *(char**)left;
	char* r = *(char**)right;

	return strcmp(l, r);
}

BEGCMP(phwllABcomp){
	DEFLR(hwll);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwllREVcomp){
	DEFLR(hwll);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	return 0;
}
BEGCMP(ptriplecomp){
	DEFLR(hwllc);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleREVcomp){
	DEFLR(hwllc);
	CMPRET(l.b, r.b);
	CMPRET(l.a, r.a);
	CMPRET(l.c, r.c);
	return 0;
}
BEGCMP(ptripleCABcomp){
	DEFLR(hwllc);
	CMPRET(l.c, r.c);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}
BEGCMP(phwrealcomp){
	DEFLR(hwreal);
	CMPRET(l.a, r.a);
	CMPRET(l.b, r.b);
	return 0;
}

int32_t pquadcomp (const void *left, const void *right) {
	linell l = *(linell*)left;
	linell r = *(linell*)right;

	sll ac = phwllABcomp(&(l.a), &(r.a));
	if (ac) return ac;
	sll bc = phwllABcomp(&(l.b), &(r.b));
	if (bc) return bc;

	return 0;
}
int32_t pfracomp (const void *left, const void *right) {
	hwllc l = *(hwllc*)left;
	hwllc r = *(hwllc*)right;

	CMPRET(l.a * r.b, l.b * r.a);
	return 0;
}
bool isinrange (sll left, sll x, sll right) {
	return (left <= x && x <= right);
}

bool isinrange_soft (sll left, sll x, sll right) {
	return (left <= x && x <= right) || (left >= x && x >= right);
}

void sw (sll *l, sll *r) {
	if (*l == *r) return;
	sll t = *l;
	*l = *r;
	*r = t;
}

ull frac[N_MAX * 3], invf[N_MAX * 3];
ull ncr (sll n, sll r, ull m) {
	if (n < 0 || r < 0 || n < r) return 0;
	return frac[n] * (invf[r] * invf[n - r] % m) % m;
}

sll a[N_MAX + 5];
// ull a[N_MAX + 5];
// sll a[3001][3001];
sll b[N_MAX + 5];
// ull b[N_MAX + 5];
// sll b[3001][3001];
sll c[N_MAX + 5];
sll d[N_MAX + 5];
sll e[N_MAX * 4];
// char s[N_MAX + 1];
char s[3010][3010];
char t[N_MAX + 1];
// char t[3010][3010];
char u[N_MAX + 1];
hwll xy[N_MAX + 5];
hwllc tup[N_MAX + 5];
sll table[3005][3005];
ull gin[N_MAX];
// here we go

ull parent[N_MAX], size[N_MAX];
void init (ull n) {
	for (sll i = 0; i < n; i++) {
		parent[i] = i;
		size[i] = 1;
	}
}
ull find (ull x) {
	if (parent[x] == x) return x;
	return parent[x] = find(parent[x]);
}
bool unite (ull a, ull b) {
	a = find(a);
	b = find(b);

	if (a == b) return false;

	if (size[a] < size[b]) {
		ull t = a;
		a = b;
		b = t;
	}
	parent[b] = a;
	size[a] += size[b];
	return true;
}

ull color[N_MAX];
bool dfs (ull v) {
	for (sll i = 0; i < n; i++) {
		if (s[v][i] == '0') continue;

		if (color[i] == color[v]) return false;
		if (color[i] == 0) {
			color[i] = 3 - color[v];
			if (!dfs(i)) return false;
		}
	}
	return true;
}

ull wf[300][300];

ull solve () {
	sll i, j, ki, li;
	// ull result = 0;
	sll result = 0;
	double dresult = 0;
	// ull maybe = 0;
	sll maybe = 0;
	// ull sum = 0;
	sll sum = 0;
	sll item;
	sll *dpcell;

	color[0] = 1;
	if (!dfs(0)) {
		puts("-1");
		return 0;
	}

	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {
			if (i == j) {
				wf[i][j] = 0;
			} else if (s[i][j] == '1') {
				wf[i][j] = 1;
			} else {
				wf[i][j] = VERYBIG;
			}
		}
	}
			for (ki = 0; ki < n; ki++) {
	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {
				wf[i][j] = smin(wf[i][j], wf[i][ki] + wf[ki][j]);
			}
		}
	}
	for (i = 0; i < n; i++) {
		for (j = 0; j < n; j++) {
			result = smax(result, wf[i][j]);
		}
	}
	result++;

	printf("%lld\n", result);
	// printf("%.15f\n", dresult);
	// puts(s);

	return 0;

	success:
	puts("YES");
	// puts("Yes");
	// printf("%llu\n", result);
	// puts("0");
	// puts("First");
	return 0;

	fail:
	puts("NO");
	// puts("No");
	// puts("0");
	// puts("-1");
	// puts("-1 -1 -1");
	// puts("Second");
	return 1;
}

int32_t main (int argc, char *argv[]) {
	int32_t i, j;

	n = 3;
	m = 0;

	// scanf("%llu", &m);
	// scanf("%llu%llu", &h, &w);
	scanf("%llu", &n, &m);
	// scanf("%llu", &k, &n, &m);
	// scanf("%llu%llu", &h, &w);
	// scanf("%llu", &q);
	// scanf("%lld%lld", &va, &vb, &vc, &vd);
	// va--;
	// vb--;
	// scanf("%llu%llu%llu%llu", &ua, &ub, &uc, &ud, &ue);
	// scanf("%s", s);
	// scanf("%s", t);
	// scanf("%s", u);
	// scanf("%llu", &k);
	// scanf("%lld", &m);
	// for (i = 0; i < n; i++) {
	// 	// scanf("%lld", &a[i]);
	// 	scanf("%lld", &d[i]);
	// }
	// scanf("%llu", &q);
	for (i = 0; i < 0; i++) {
		// scanf("%lld%lld", &xy[i].a, &xy[i].b);
		// scanf("%lld%lld%lld", &tup[i].a, &tup[i].b, &tup[i].c);
		// scanf("%lld", &c[i]);

		scanf("%lld", &a[i]);
		// scanf("%lld", &b[i]);
		// scanf("%lld", &c[i]);
		// scanf("%lld", &d[i]);
		// a[i]--;
		// b[i]--;
		// c[i]--;
		// d[i]--;
		// xy[i].a--;
		// xy[i].b--;
		// tup[i].a--;
		// tup[i].b--;
	}
	// scanf("%lld%lld", &va, &vb);
	// scanf("%llu", &m);
	// scanf("%llu", &q);
	// scanf("%s", s);
	// for (i = 0; i < n; i++) {
	// 	// scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	// xy[i].a--;
	// 	// xy[i].b--;
	// 	// scanf("%lld", &a[i], &b[i]);
	// 	// scanf("%lld", &b[i]);
	// 	// a[i]--;
	// 	// b[i]--;
	// 	scanf("%lld", &c[i]);
	// 	scanf("%lld", &d[i]);
	// 	// scanf("%lld", &e[i]);
	// 	c[i]--;
	// 	d[i]--;
	// }

	// for (i = 0; i < q; i++) {
	// 	// scanf("%lld%lld", &xy[i].a, &xy[i].b);
	// 	scanf("%lld", &c[i]);
	// 	// xy[i].a--;
	// 	// xy[i].b--;
	// }

	// for (i = 0; i < h; i++) {
	// 	for (j = 0; j < w; j++) {
	// 		scanf("%lld", &table[i][j]);
	// 		// table[i][j]--;
	// 	}
	// }
	for (i = 0; i < n; i++) {
		scanf("%s", s[i]);
	}
	// scanf("%llu", &q);

	solve();

	return 0;
}