Beauty of Array

The beauty of an array a of length m is defined as the number of integers i (0 ≤ i < m) such that:

a[i] == i

You are given an array arr of n integers. You can perform the following operation any number of times:

• Choose some index i (0 ≤ i < length of the array) and delete arr[i], without changing the order of the remaining elements.

Your task is to find the maximum possible beauty of the resulting array.

Function Description

Complete the function maximizeBeauty in the editor below.

def maximizeBeauty(arr: List[int]) -> int:

Parameters

• arr[n]: the given array of integers

Returns

• int: the maximum possible beauty of the array

Constraints

• 1 ≤ n ≤ 2000
• 1 ≤ arr[i] ≤ 10^9

Example

Input: arr = [1, 3, 2, 5, 4, 5, 3]

One optimal sequence of operations is:

1. Delete arr[2] = 2
2. Delete arr[6] = 3

Resulting array:

csharp复制编辑[1, 3, 5, 4, 5]

Now, the beauty of the array is 4, since:

• arr[0] = 1
• arr[1] = 3
• arr[3] = 4
• arr[4] = 5
  → these all satisfy arr[i] == i for their respective indices.

Return 4.

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