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#include<iostream>
#include<queue>

#define INF 500

bool edge[400][400]; // [from][to]
int distance[400][400]; // [from][to]
int size;

struct CategoryEdge {
    int from;
    int to;
};

CategoryEdge categories[400][160000]; // [distance][index]
int categorySizes[400]; // [category]

void BFS(int start) {
    std::queue<int> q;
    for (int i = 0; i < size; i++) {
        distance[start][i] = INF;
    }
    distance[start][start] = 0;
    q.push(start);
    while (!q.empty()) {
        int current = q.front();
        q.pop();
        for (int i = 0; i < size; i++) {
            if (edge[current][i] && distance[start][i] == INF) {
                distance[start][i] = distance[start][current] + 1;
                q.push(i);
            }
        }
    }
}

int getDiameterWithTeleport(int teleport1, int teleport2, int upperBound) {
    int diameter = 0;
    for (int i = size - 1; i > diameter; i--) {
        for (int j = 0; j < categorySizes[i]; j++) {
            int from = categories[i][j].from;
            int to = categories[i][j].to;
            diameter = std::max(diameter, std::min(distance[from][to], std::min(distance[from][teleport1] + distance[to][teleport2], distance[from][teleport2] + distance[to][teleport1])));
            if (diameter >= upperBound) {
                return upperBound;
            }
        }
    }
    return diameter;
}

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(NULL);
    int t;
    std::cin >> t;
    for (int i = 0; i < t; i++) {
        std::cin >> size;
        for (int j = 0; j < size; j++) {
            for (int k = 0; k < size; k++) {
                char c;
                std::cin >> c;
                edge[j][k] = c == '1';
            }
        }

        for (int j = 0; j < size; j++) {
            BFS(j);
        }

        for (int j = 0; j < size; j++) {
            categorySizes[j] = 0;
        }

        for (int j = 0; j < size; j++) {
            for (int k = 0; k < j; k++) {
                categories[distance[j][k]][categorySizes[distance[j][k]]].from = j;
                categories[distance[j][k]][categorySizes[distance[j][k]]].to = k;
                categorySizes[distance[j][k]]++;
            }
        }

        int minDiameter = INF;
        for (int j = 0; j < size; j++) {
            for (int k = 0; k < j; k++) {
                minDiameter = getDiameterWithTeleport(j, k, minDiameter);
            }
        }

        std::cout << minDiameter << "\n";
    }
    return 0;
}