1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
#include <bits/stdc++.h>
using namespace std;
#define st first
#define nd second
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define BOOST ios_base::sync_with_stdio(0), cin.tie(0)
typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;

const int N = 405, inf = 1e9;
int g[N][N];
int d[N][N];
int tmp[N][N];
int t[N][N][N];
vector<int> xd[N];
int n;

void solve(){
	cin >> n;
	for(int i=1; i<=n; i++){
		string s; cin >> s;
		s = '#' + s;
		for(int j=1; j<=n; j++){
			if(s[j] == '1'){
				g[i][j] = 1;
			}
			else{
				g[i][j] = 0;
			}
		}
	}

	// warshall
	for(int i=1; i<=n; i++){
		for(int j=1; j<=n; j++){
			d[i][j] = inf;
			if(g[i][j]) d[i][j] = 1;

			for(int k=1; k<=n; k++) t[i][j][k] = 0;
		}
		d[i][i] = 0;
	}
	for(int k=1; k<=n; k++){
		for(int i=1; i<=n; i++){
			for(int j=1; j<=n; j++){
				if(d[i][k] + d[k][j] < d[i][j]){
					d[i][j] = d[i][k] + d[k][j];
				}
			}
		}
	}

	for(int i=1; i<=n; i++){
		xd[i] = vector<int>(n);
		iota(all(xd[i]), 1);
		sort(all(xd[i]), [&](int a, int b){return d[i][a] < d[i][b];});
	}
	
	for(int i=1; i<=n; i++){
		for(int j=1; j<=n; j++){
			int a = 0, b = n-1;
			for(int k=1; k<=n; k++){ // fuel buget 
				while(b >= 0 && (d[i][xd[j][b]] <= k)) b--;
				while(a < n && (b == -1 || d[i][xd[i][a]] + d[j][xd[j][b]] <= k)){
					tmp[xd[i][a]][j] = k;
					a++;
				}
			}
		}
		for(int j=1; j<=n; j++){
			for(int k=1; k<=n; k++){
				if(j == k) continue;
				int x = min(tmp[j][k], tmp[k][j]);
				t[x][j][k]++;
			}
		}
	}
	for(int i=1; i<=n; i++){
		for(int j=1; j<=n; j++){
			for(int k=1; k<=n; k++){
				if(j == k) continue;
				t[i][j][k] += t[i-1][j][k];
				if(t[i][j][k] == n){
					cout << i << "\n";
					return;
				}
			}
		}
	}
}

int main(){
	BOOST;
	int q; cin >> q;
	while(q--) solve();
}