// LeetCode 3025: Find The Number Of Ways To Place People I
// 難度: Medium
// 日期: 2025-09-02

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

public class Solution
{
    public int NumberOfPairs(int[][] points)
    {
        // 遍歷所有點對 (A, B)
        // 檢查每個pair形成的矩形, 裡面跟邊界會不會包含其他點

        // points[0].Length == 2
        int n = points.Length;
        int count = 0;

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

                int[] pointA = points[i];
                int[] pointB = points[j];

                // check if A.x <= B.x && A.y >= B.y
                // if yes, check if any points in rectangle
                if (pointA[0] <= pointB[0] && pointA[1] >= pointB[1])
                {
                    // difinition of border
                    bool hasOtherPoint = false;
                    int minX = pointA[0];
                    int maxX = pointB[0];
                    int minY = pointB[1];
                    int maxY = pointA[1];

                    // check other point if its in border
                    for (var k = 0; k < n; k++)
                    {
                        if (k == i || k == j) continue;

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

                    if (!hasOtherPoint) count++;
                }
            }
        }
        return count;
    }
}

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}");
    }
}