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#include <bits/stdc++.h>
using namespace std;
const int MXN = 401;
short d[MXN][MXN];
short pref[MXN][MXN][MXN];
short suf[MXN][MXN][MXN];
int main()
{
	ios_base::sync_with_stdio(false);
	cin.tie(NULL);
	int t; cin>>t;
	while (t--)
	{
		int n; cin>>n;
		//~ vector d(n+1, vector(n+1, (short)0));
		for (int i=1; i<=n; i++)
		{
			for (int j=1; j<=n; j++)
			{
				char x; cin>>x;
				if (i == j) d[i][j] = 0;
				else d[i][j] = x == '1' ? 1 : 1000;
			}
		}
		for (int k=1; k<=n; k++)
		{
			for (int i=1; i<=n; i++)
			{
				for (int j=1; j<=n; j++)
				{
					d[i][j] = min(d[i][j], (short)(d[i][k] + d[k][j]));
				}
			}
		}
		
		for (int i=1; i<=n; i++)
		{
			for (int j=1; j<=n; j++)
			{
				memset(pref[i][j], 0, sizeof(short) * (n + 1));
				memset(suf[i][j], 0, sizeof(short) * (n + 1));
			}
		}
		//~ for (int i=1; i<=n; i++)
		//~ {
			//~ for (int j=1; j<=n; j++)
			//~ {
				//~ for (int l=1; l<=n; l++)
				//~ {
					//~ assert(!pref[i][j][l]);
					//~ assert(!suf[i][j][l]);
				//~ }
			//~ }
		//~ }
		//~ vector pref(n+1, vector(n+1, vector(n+1, (short)0)));
		//~ vector suf(n+1, vector(n+1, vector(n+2, (short)0)));
		for (int i=1; i<=n; i++)
		{
			for (int j=1; j<=n; j++)
			{
				for (int l=1; l<=n; l++)
				{
					short d1 = d[i][l];
					short d2 = d[j][l];
					if (d2 < d1)
					{
						if (pref[i][j][d1 - d2] < d1)
							pref[i][j][d1 - d2] = d1;
						if (suf[i][j][d1 - d2] < d2)
							suf[i][j][d1 - d2] = d2;
					}
					else if (d1 > pref[i][j][0])
					{
						pref[i][j][0] = d1;
					}
				}
				for (int l=1; l<=n; l++)
					pref[i][j][l] = max(pref[i][j][l-1], pref[i][j][l]);
				for (int l=n; l>=1; l--)
					suf[i][j][l] = max(suf[i][j][l+1], suf[i][j][l]);
			}
		}
		
		short ans = n+1;
		for (int i=1; i<=n; i++)
		{
			for (int j=i+1; j<=n; j++)
			{
				short pom = 0;
				for (int l=1; l<=n; l++)
				{
					short remo = d[i][l] > d[j][l] ? i : j;
					short dist = min(d[i][l], d[j][l]);
					pom = max({pom, pref[l][remo][dist], (short)(dist + suf[l][remo][dist])});
				}
				ans = min(ans, pom);
			}
		}
		cout<<ans<<"\n";
	}
}