// LeetCode 3027: Find The Number Of Ways To Place People Ii
// 難度: Hard
// 日期: 2025-09-03

using System;
using System.Collections.Generic;
using System.Linq;

public class Solution {
    public int NumberOfPairs(int[][] points)
    {
        int n = points.Length;
        int result = 0;

        for (var i = 0; i < n; i++)
        {
            for (var j = 0; j < n; j++)
            {
                if (i == j) continue;

                // 判斷 Alice points[i] 是否在 Bob points[j] 左上角
                var Alice = points[i];
                var Bob = points[j];
                if (Alice[0] <= Bob[0] && Alice[1] >= Bob[1])
                {
                    // get border
                    int minX = Alice[0];
                    int maxX = Bob[0];
                    int minY = Bob[1];
                    int maxY = Alice[1];
                    bool isAnyPerson = false;

                    for (var k = 0; k < n; k++)
                    {
                        if (i == k || j == k) continue;

                        var person = points[k];
                        if (minX <= person[0] && person[0] <= maxX && minY <= person[1] && person[1] <= maxY)
                        {
                            isAnyPerson = true;
                            break;
                        }
                    }

                    if (!isAnyPerson) result++;
                }
            }
        }
        return result;
    }
}

public class Program {
    public static void Main() {
        Solution solution = new Solution();

        // 測試案例
        TestCase(solution);
    }
    
    static void TestCase(Solution solution) {
        // Input: 
        int[][] points = new int[][] {
            new int[] {6, 2},
            new int[] {4, 4},
            new int[] {2, 6}
        };
        // Expected: 
        Console.WriteLine($"Test Case: [[6,2],[4,4],[2,6]]");
        Console.WriteLine($"Expected: 2");

        // Actual: 
        int result1 = solution.NumberOfPairs(points);
        Console.WriteLine($"Result: {result1}");
    }
}