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/**
 * Finds the next "beautiful" number greater than the given input.
 * A beautiful number is defined as one where each digit appears exactly as many times as its value.
 * For example, 22 is beautiful because digit 2 appears twice.
 *
 * @param {number} n - The input number.
 * @return {number} - The next beautiful number greater than n.
 */
var nextBeautifulNumber = function(n) {
    // Precomputed list of beautiful numbers in ascending order.

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/**
 * @param {string} s
 * @return {boolean}
 */
var hasSameDigits = function(s) {
    // Convert the input string into an array of digits (as numbers)
    let digits = s.split('').map(Number);

    // Repeat the transformation until only two digits remain
    while (digits.length > 2) {

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/**
 * @param {number[]} nums
 * @param {number} k
 * @param {number} numOperations
 * @return {number}
 */
var maxFrequency = function (nums, k, numOperations) {
    // Sort the array to enable binary search and range grouping
    nums.sort((a, b) => a - b);

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/**
 * @param {number[]} nums - The input array of integers
 * @param {number} k - The maximum value that can be added/subtracted in one operation
 * @param {number} numOperations - The total number of operations allowed
 * @return {number} - The maximum frequency of any element after operations
 */
var maxFrequency = function(nums, k, numOperations) {
    const n = nums.length;

    // Sort the array to enable binary search and range grouping

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/**
 * @param {string[]} operations
 * @return {number}
 */
var finalValueAfterOperations = function(operations) {
    // Step 1: Initialize the variable X to 0
    let X = 0;

    // Step 2: Loop through each operation in the array
    for (let i = 0; i < operations.length; i++) {

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/**
 * @param {string} s
 * @param {number} a
 * @param {number} b
 * @return {string}
 */
var findLexSmallestString = function(s, a, b) {
    // Set to keep track of visited strings to avoid revisiting the same state
    const visited = new Set();

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/**
 * Calculates the maximum number of partitions after performing operations
 * that allow up to `k` distinct characters per partition.
 *
 * @param {string} s - Input string consisting of lowercase letters.
 * @param {number} k - Maximum number of distinct characters allowed per partition.
 * @return {number} - Maximum number of partitions achievable.
 */
var maxPartitionsAfterOperations = function(s, k) {
    const n = s.length;

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/**
 * @param {number[]} nums
 * @param {number} value
 * @return {number}
 */
var findSmallestInteger = function(nums, value) {
    // Step 1: Create a frequency map to count how many times each remainder appears
    const freq = new Map();

    for (let num of nums) {

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/**
 * @param {number[]} nums
 * @return {number}
 */
var maxIncreasingSubarrays = function (nums) {
    let maxK = 0;       // Stores the maximum valid k found so far
    let curLen = 1;     // Length of the current strictly increasing run
    let prevLen = 0;    // Length of the previous strictly increasing run

    for (let i = 1; i < nums.length; i++) {

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/**
 * @param {number[]} nums
 * @param {number} k
 * @return {boolean}
 */
var hasIncreasingSubarrays = function(nums, k) {
    // Helper function to check if a subarray is strictly increasing
    function isStrictlyIncreasing(start, end) {
        for (let i = start; i < end; i++) {
            if (nums[i] >= nums[i + 1]) {