Find the Number of Ways to Place People II
<p>You are given a 2D array <code>points</code> of size <code>n x 2</code> representing integer coordinates of some points on a 2D-plane, where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>.</p>

<p>We define the <strong>right</strong> direction as positive x-axis (<strong>increasing x-coordinate</strong>) and the <strong>left</strong> direction as negative x-axis (<strong>decreasing x-coordinate</strong>). Similarly, we define the <strong>up</strong> direction as positive y-axis (<strong>increasing y-coordinate</strong>) and the <strong>down</strong> direction as negative y-axis (<strong>decreasing y-coordinate</strong>)</p>

<p>You have to place <code>n</code> people, including Alice and Bob, at these points such that there is <strong>exactly one</strong> person at every point. Alice wants to be alone with Bob, so Alice will build a rectangular fence with Alice&#39;s position as the <strong>upper left corner</strong> and Bob&#39;s position as the <strong>lower right corner</strong> of the fence (<strong>Note</strong> that the fence <strong>might not</strong> enclose any area, i.e. it can be a line). If any person other than Alice and Bob is either <strong>inside</strong> the fence or <strong>on</strong> the fence, Alice will be sad.</p>

<p>Return <em>the number of <strong>pairs of points</strong> where you can place Alice and Bob, such that Alice <strong>does not</strong> become sad on building the fence</em>.</p>

<p><strong>Note</strong> that Alice can only build a fence with Alice&#39;s position as the upper left corner, and Bob&#39;s position as the lower right corner. For example, Alice cannot build either of the fences in the picture below with four corners <code>(1, 1)</code>, <code>(1, 3)</code>, <code>(3, 1)</code>, and <code>(3, 3)</code>, because:</p>

<ul>
	<li>With Alice at <code>(3, 3)</code> and Bob at <code>(1, 1)</code>, Alice&#39;s position is not the upper left corner and Bob&#39;s position is not the lower right corner of the fence.</li>
	<li>With Alice at <code>(1, 3)</code> and Bob at <code>(1, 1)</code>, Bob&#39;s position is not the lower right corner of the fence.</li>
</ul>
<img alt="" src="https://assets.leetcode.com/uploads/2024/01/04/example0alicebob-1.png" style="width: 750px; height: 308px;padding: 10px; background: #fff; border-radius: .5rem;" />
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/01/04/example1alicebob.png" style="width: 376px; height: 308px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem;" />
<pre>
<strong>Input:</strong> points = [[1,1],[2,2],[3,3]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no way to place Alice and Bob such that Alice can build a fence with Alice&#39;s position as the upper left corner and Bob&#39;s position as the lower right corner. Hence we return 0. 
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/02/04/example2alicebob.png" style="width: 1321px; height: 363px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem;" />
<pre>
<strong>Input:</strong> points = [[6,2],[4,4],[2,6]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are two ways to place Alice and Bob such that Alice will not be sad:
- Place Alice at (4, 4) and Bob at (6, 2).
- Place Alice at (2, 6) and Bob at (4, 4).
You cannot place Alice at (2, 6) and Bob at (6, 2) because the person at (4, 4) will be inside the fence.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2024/02/04/example4alicebob.png" style="width: 1123px; height: 308px; padding: 10px; background: rgb(255, 255, 255); border-radius: 0.5rem;" />
<pre>
<strong>Input:</strong> points = [[3,1],[1,3],[1,1]]
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are two ways to place Alice and Bob such that Alice will not be sad:
- Place Alice at (1, 1) and Bob at (3, 1).
- Place Alice at (1, 3) and Bob at (1, 1).
You cannot place Alice at (1, 3) and Bob at (3, 1) because the person at (1, 1) will be on the fence.
Note that it does not matter if the fence encloses any area, the first and second fences in the image are valid.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= n &lt;= 1000</code></li>
	<li><code>points[i].length == 2</code></li>
	<li><code>-10<sup>9</sup> &lt;= points[i][0], points[i][1] &lt;= 10<sup>9</sup></code></li>
	<li>All <code>points[i]</code> are distinct.</li>
</ul>

['rectangle-area']
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    int numberOfPairs(vector<vector<int>>& points) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public int numberOfPairs(int[][] points) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def numberOfPairs(self, points):\n        \"\"\"\n        :type points: List[List[int]]\n        :rtype: int\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def numberOfPairs(self, points: List[List[int]]) -> int:\n        "}, {"value": "c", "text": "C", "defaultCode": "int numberOfPairs(int** points, int pointsSize, int* pointsColSize) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public int NumberOfPairs(int[][] points) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {number[][]} points\n * @return {number}\n */\nvar numberOfPairs = function(points) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function numberOfPairs(points: number[][]): number {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param Integer[][] $points\n     * @return Integer\n     */\n    function numberOfPairs($points) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func numberOfPairs(_ points: [[Int]]) -> Int {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun numberOfPairs(points: Array<IntArray>): Int {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  int numberOfPairs(List<List<int>> points) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func numberOfPairs(points [][]int) int {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {Integer[][]} points\n# @return {Integer}\ndef number_of_pairs(points)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def numberOfPairs(points: Array[Array[Int]]): Int = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn number_of_pairs(points: Vec<Vec<i32>>) -> i32 {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (number-of-pairs points)\n  (-> (listof (listof exact-integer?)) exact-integer?)\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec number_of_pairs(Points :: [[integer()]]) -> integer().\nnumber_of_pairs(Points) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec number_of_pairs(points :: [[integer]]) :: integer\n  def number_of_pairs(points) do\n    \n  end\nend"}]
{
  "name": "numberOfPairs",
  "params": [
    {
      "name": "points",
      "type": "integer[][]"
    }
  ],
  "return": {
    "type": "integer"
  }
}
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Using compile arguments: <code>--enable-preview --release 21</code></p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>"], "python": ["Python", "<p><code>Python 2.7.18</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/2/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/2/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/2/library/collections.html\" target=\"_blank\">collections</a>. 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For the latest Python, please choose Python3 instead.</p>"], "c": ["C", "<p>Compiled with <code>gcc 14</code> using the gnu11 standard.</p>\r\n\r\n<p>Your code is compiled with level one optimization (<code>-O2</code>). <a href=\"https://github.com/google/sanitizers/wiki/AddressSanitizer\" target=\"_blank\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n\r\n<p>For hash table operations, you may use <a href=\"https://troydhanson.github.io/uthash/\" target=\"_blank\">uthash</a>. \"uthash.h\" is included by default. Below are some examples:</p>\r\n\r\n<p><b>1. Adding an item to a hash.</b>\r\n<pre>\r\nstruct hash_entry {\r\n    int id;            /* we'll use this field as the key */\r\n    char name[10];\r\n    UT_hash_handle hh; /* makes this structure hashable */\r\n};\r\n\r\nstruct hash_entry *users = NULL;\r\n\r\nvoid add_user(struct hash_entry *s) {\r\n    HASH_ADD_INT(users, id, s);\r\n}\r\n</pre>\r\n</p>\r\n\r\n<p><b>2. Looking up an item in a hash:</b>\r\n<pre>\r\nstruct hash_entry *find_user(int user_id) {\r\n    struct hash_entry *s;\r\n    HASH_FIND_INT(users, &user_id, s);\r\n    return s;\r\n}\r\n</pre>\r\n</p>\r\n\r\n<p><b>3. Deleting an item in a hash:</b>\r\n<pre>\r\nvoid delete_user(struct hash_entry *user) {\r\n    HASH_DEL(users, user);  \r\n}\r\n</pre>\r\n</p>"], "csharp": ["C#", "<p><a href=\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-13\" target=\"_blank\">C# 13</a> with .NET 9 runtime</p>"], "javascript": ["JavaScript", "<p><code>Node.js 22.14.0</code>.</p>\r\n\r\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\"http://node.green/\" target=\"_blank\">new ES6 features</a>.</p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "ruby": ["Ruby", "<p><code>Ruby 3.2</code></p>\r\n\r\n<p>Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms</p>"], "swift": ["Swift", "<p><code>Swift 6.0</code>.</p>\r\n\r\n<p>You may use the following packages:<br/>\r\n<a href=\"https://github.com/apple/swift-algorithms/tree/1.2.0\" target=\"_blank\">swift-algorithms 1.2.0</a><br/>\r\n<a href=\"https://github.com/apple/swift-collections/tree/1.1.4\" target=\"_blank\">swift-collections 1.1.4</a><br/>\r\n<a href=\"https://github.com/apple/swift-numerics/tree/1.0.2\" target=\"_blank\">swift-numerics 1.0.2</a></p>"], "golang": ["Go", "<p><code>Go 1.23</code></p>\r\n<p>Support <a href=\"https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1</a> and <a href=\"https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha</a> library.</p>"], "python3": ["Python3", "<p><code>Python 3.11</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/3/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/3/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/3/library/collections.html\" target=\"_blank\">collections</a>. If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>"], "scala": ["Scala", "<p><code>Scala 3.3.1</code>.</p>"], "kotlin": ["Kotlin", "<p><code>Kotlin 2.1.10</code>.</p>"], "rust": ["Rust", "<p><code>Rust 1.85.0</code>. Your code will be compiled with <code>opt-level</code> 2.</p>\r\n\r\n<p>Supports <a href=\"https://crates.io/crates/rand\" target=\"_blank\">rand v0.8</a> and <a href=\"https://crates.io/crates/regex\" target=\"_blank\">regex\u00a0v1</a> and <a href=\"https://crates.io/crates/itertools\" target=\"_blank\">itertools\u00a0v0.14</a> from crates.io</p>"], "php": ["PHP", "<p><code>PHP 8.2</code>.</p>\r\n<p>With bcmath module</p>"], "typescript": ["Typescript", "<p><code>TypeScript 5.7.3, Node.js 22.14.0</code>.</p>\r\n\r\n<p>Compile Options: <code>--alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2024</code></p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "racket": ["Racket", "<p><a href=\"https://docs.racket-lang.org/guide/performance.html#%28tech._c%29\" target=\"_blank\">Racket CS</a> v8.15</p>\r\n\r\n<p>Using <code>#lang racket</code></p>\r\n\r\n<p>Required <code>data/gvector data/queue data/order data/heap</code> automatically for your convenience</p>"], "erlang": ["Erlang", "Erlang/OTP 26"], "elixir": ["Elixir", "Elixir 1.17 with Erlang/OTP 26"], "dart": ["Dart", "<p>Dart 3.2. You may use package <a href=\"https://pub.dev/packages/collection/versions/1.18.0\" target=\"_blank\">collection</a></p>\r\n\r\n<p>Your code will be run directly without compiling</p>"]}
['Array', 'Math', 'Geometry', 'Sorting', 'Enumeration']