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#include <iostream>
#include <vector>
#include <queue>
#include <cmath>

class Solution {
public:
    int maxPartitionFactor(std::vector<std::vector<int>>& points) {
        int n = points.size();
        if (n == 2) {
            return 0;
        }
        
        std::vector<std::vector<int>> graph(n, std::vector<int>(n, 0x7fff'ffff));
        int left = 0, right = 0;
        for (int i = 0; i < n - 1; ++i) {
            for (int j = i + 1; j < n; ++j) {
                graph[i][j] = graph[j][i] = mdist(points[i], points[j]);
                right = std::max(graph[i][j], right);
            }
        }
        
        while (right >= left) {
            int mid = (left + right) / 2;
            if (check(graph, n, mid)) {
                left = mid + 1;
            }
            else {
                right = mid - 1;
            }
        }
        
        return right;
    }
    
private:
    bool check(std::vector<std::vector<int>>& graph, int n, int minDist) {
        std::vector<int> visited(n, 0);
        std::queue<int> q;
        for (int i = 0; i < n; ++i) {
            if (visited[i]) {
                continue;
            }
            visited[i] = 1;
            q.push(i);
            while (!q.empty()) {
                int u = q.front();
                q.pop();
                for (int v = 0; v < n; ++v) {
                    if (graph[u][v] >= minDist) {
                        continue;
                    }
                    if (visited[v] == 0) {
                        visited[v] = -visited[u];
                        q.push(v);
                    }
                    else if (visited[v] == visited[u]) {
                        return false;
                    }
                }
            }
        }
        return true;
    }
    
    int mdist(std::vector<int>& a, std::vector<int>& b) {
        return std::abs(a[0] - b[0]) + std::abs(a[1] - b[1]);
    }
};