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<p>You are given a string <code>num</code> representing a large integer. An integer is <strong>good</strong> if it meets the following conditions:</p>
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<ul>
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<li>It is a <strong>substring</strong> of <code>num</code> with length <code>3</code>.</li>
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<li>It consists of only one unique digit.</li>
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</ul>
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<p>Return <em>the <strong>maximum good </strong>integer as a <strong>string</strong> or an empty string </em><code>""</code><em> if no such integer exists</em>.</p>
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<p>Note:</p>
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<ul>
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<li>A <strong>substring</strong> is a contiguous sequence of characters within a string.</li>
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<li>There may be <strong>leading zeroes</strong> in <code>num</code> or a good integer.</li>
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</ul>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> num = "6<strong><u>777</u></strong>133339"
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<strong>Output:</strong> "777"
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<strong>Explanation:</strong> There are two distinct good integers: "777" and "333".
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"777" is the largest, so we return "777".
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> num = "23<strong><u>000</u></strong>19"
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<strong>Output:</strong> "000"
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<strong>Explanation:</strong> "000" is the only good integer.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> num = "42352338"
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<strong>Output:</strong> ""
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<strong>Explanation:</strong> No substring of length 3 consists of only one unique digit. Therefore, there are no good integers.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>3 <= num.length <= 1000</code></li>
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<li><code>num</code> only consists of digits.</li>
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</ul>
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<p>A parentheses string is a <strong>non-empty</strong> string consisting only of <code>'('</code> and <code>')'</code>. It is <strong>valid</strong> if <strong>any</strong> of the following conditions is <strong>true</strong>:</p>
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<ul>
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<li>It is <code>()</code>.</li>
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<li>It can be written as <code>AB</code> (<code>A</code> concatenated with <code>B</code>), where <code>A</code> and <code>B</code> are valid parentheses strings.</li>
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<li>It can be written as <code>(A)</code>, where <code>A</code> is a valid parentheses string.</li>
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</ul>
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<p>You are given an <code>m x n</code> matrix of parentheses <code>grid</code>. A <strong>valid parentheses string path</strong> in the grid is a path satisfying <strong>all</strong> of the following conditions:</p>
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<ul>
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<li>The path starts from the upper left cell <code>(0, 0)</code>.</li>
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<li>The path ends at the bottom-right cell <code>(m - 1, n - 1)</code>.</li>
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<li>The path only ever moves <strong>down</strong> or <strong>right</strong>.</li>
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<li>The resulting parentheses string formed by the path is <strong>valid</strong>.</li>
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</ul>
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<p>Return <code>true</code> <em>if there exists a <strong>valid parentheses string path</strong> in the grid.</em> Otherwise, return <code>false</code>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2022/03/15/example1drawio.png" style="width: 521px; height: 300px;" />
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<pre>
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<strong>Input:</strong> grid = [["(","(","("],[")","(",")"],["(","(",")"],["(","(",")"]]
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<strong>Output:</strong> true
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<strong>Explanation:</strong> The above diagram shows two possible paths that form valid parentheses strings.
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The first path shown results in the valid parentheses string "()(())".
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The second path shown results in the valid parentheses string "((()))".
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Note that there may be other valid parentheses string paths.
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</pre>
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<p><strong>Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2022/03/15/example2drawio.png" style="width: 165px; height: 165px;" />
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<pre>
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<strong>Input:</strong> grid = [[")",")"],["(","("]]
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<strong>Output:</strong> false
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<strong>Explanation:</strong> The two possible paths form the parentheses strings "))(" and ")((". Since neither of them are valid parentheses strings, we return false.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>m == grid.length</code></li>
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<li><code>n == grid[i].length</code></li>
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<li><code>1 <= m, n <= 100</code></li>
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<li><code>grid[i][j]</code> is either <code>'('</code> or <code>')'</code>.</li>
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</ul>
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<p>Given the <code>root</code> of a binary tree, return <em>the number of nodes where the value of the node is equal to the <strong>average</strong> of the values in its <strong>subtree</strong></em>.</p>
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<p><strong>Note:</strong></p>
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<ul>
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<li>The <strong>average</strong> of <code>n</code> elements is the <strong>sum</strong> of the <code>n</code> elements divided by <code>n</code> and <strong>rounded down</strong> to the nearest integer.</li>
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<li>A <strong>subtree</strong> of <code>root</code> is a tree consisting of <code>root</code> and all of its descendants.</li>
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</ul>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img src="https://assets.leetcode.com/uploads/2022/03/15/image-20220315203925-1.png" style="width: 300px; height: 212px;" />
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<pre>
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<strong>Input:</strong> root = [4,8,5,0,1,null,6]
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<strong>Output:</strong> 5
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<strong>Explanation:</strong>
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For the node with value 4: The average of its subtree is (4 + 8 + 5 + 0 + 1 + 6) / 6 = 24 / 6 = 4.
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For the node with value 5: The average of its subtree is (5 + 6) / 2 = 11 / 2 = 5.
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For the node with value 0: The average of its subtree is 0 / 1 = 0.
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For the node with value 1: The average of its subtree is 1 / 1 = 1.
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For the node with value 6: The average of its subtree is 6 / 1 = 6.
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</pre>
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<p><strong>Example 2:</strong></p>
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<img src="https://assets.leetcode.com/uploads/2022/03/26/image-20220326133920-1.png" style="width: 80px; height: 76px;" />
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<pre>
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<strong>Input:</strong> root = [1]
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> For the node with value 1: The average of its subtree is 1 / 1 = 1.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li>The number of nodes in the tree is in the range <code>[1, 1000]</code>.</li>
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<li><code>0 <= Node.val <= 1000</code></li>
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</ul>
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<p>Alice is texting Bob using her phone. The <strong>mapping</strong> of digits to letters is shown in the figure below.</p>
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<img alt="" src="https://assets.leetcode.com/uploads/2022/03/15/1200px-telephone-keypad2svg.png" style="width: 200px; height: 162px;" />
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<p>In order to <strong>add</strong> a letter, Alice has to <strong>press</strong> the key of the corresponding digit <code>i</code> times, where <code>i</code> is the position of the letter in the key.</p>
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<ul>
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<li>For example, to add the letter <code>'s'</code>, Alice has to press <code>'7'</code> four times. Similarly, to add the letter <code>'k'</code>, Alice has to press <code>'5'</code> twice.</li>
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<li>Note that the digits <code>'0'</code> and <code>'1'</code> do not map to any letters, so Alice <strong>does not</strong> use them.</li>
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</ul>
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<p>However, due to an error in transmission, Bob did not receive Alice's text message but received a <strong>string of pressed keys</strong> instead.</p>
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<ul>
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<li>For example, when Alice sent the message <code>"bob"</code>, Bob received the string <code>"2266622"</code>.</li>
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</ul>
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<p>Given a string <code>pressedKeys</code> representing the string received by Bob, return <em>the <strong>total number of possible text messages</strong> Alice could have sent</em>.</p>
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<p>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> pressedKeys = "22233"
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<strong>Output:</strong> 8
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<strong>Explanation:</strong>
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The possible text messages Alice could have sent are:
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"aaadd", "abdd", "badd", "cdd", "aaae", "abe", "bae", and "ce".
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Since there are 8 possible messages, we return 8.
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> pressedKeys = "222222222222222222222222222222222222"
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<strong>Output:</strong> 82876089
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<strong>Explanation:</strong>
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There are 2082876103 possible text messages Alice could have sent.
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Since we need to return the answer modulo 10<sup>9</sup> + 7, we return 2082876103 % (10<sup>9</sup> + 7) = 82876089.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= pressedKeys.length <= 10<sup>5</sup></code></li>
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<li><code>pressedKeys</code> only consists of digits from <code>'2'</code> - <code>'9'</code>.</li>
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</ul>
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