<p>You are given a <strong>0-indexed</strong> array <code>usageLimits</code> of length <code>n</code>.</p> <p>Your task is to create <strong>groups</strong> using numbers from <code>0</code> to <code>n - 1</code>, ensuring that each number, <code>i</code>, is used no more than <code>usageLimits[i]</code> times in total <strong>across all groups</strong>. You must also satisfy the following conditions:</p> <ul> <li>Each group must consist of <strong>distinct </strong>numbers, meaning that no duplicate numbers are allowed within a single group.</li> <li>Each group (except the first one) must have a length <strong>strictly greater</strong> than the previous group.</li> </ul> <p>Return <em>an integer denoting the <strong>maximum</strong> number of groups you can create while satisfying these conditions.</em></p> <p> </p> <p><strong class="example">Example 1:</strong></p> <pre> <strong>Input:</strong> <code>usageLimits</code> = [1,2,5] <strong>Output:</strong> 3 <strong>Explanation:</strong> In this example, we can use 0 at most once, 1 at most twice, and 2 at most five times. One way of creating the maximum number of groups while satisfying the conditions is: Group 1 contains the number [2]. Group 2 contains the numbers [1,2]. Group 3 contains the numbers [0,1,2]. It can be shown that the maximum number of groups is 3. So, the output is 3. </pre> <p><strong class="example">Example 2:</strong></p> <pre> <strong>Input:</strong> <code>usageLimits</code> = [2,1,2] <strong>Output:</strong> 2 <strong>Explanation:</strong> In this example, we can use 0 at most twice, 1 at most once, and 2 at most twice. One way of creating the maximum number of groups while satisfying the conditions is: Group 1 contains the number [0]. Group 2 contains the numbers [1,2]. It can be shown that the maximum number of groups is 2. So, the output is 2. </pre> <p><strong class="example">Example 3:</strong></p> <pre> <strong>Input:</strong> <code>usageLimits</code> = [1,1] <strong>Output:</strong> 1 <strong>Explanation:</strong> In this example, we can use both 0 and 1 at most once. One way of creating the maximum number of groups while satisfying the conditions is: Group 1 contains the number [0]. It can be shown that the maximum number of groups is 1. So, the output is 1. </pre> <p> </p> <p><strong>Constraints:</strong></p> <ul> <li><code>1 <= usageLimits.length <= 10<sup>5</sup></code></li> <li><code>1 <= usageLimits[i] <= 10<sup>9</sup></code></li> </ul>