Problem

Given an array arr of size n, repeatedly perform the following until the array becomes empty:

1. Choose an integer k such that 1 <= k <= current length of arr.
2. Compute the MEX of the first k elements.
3. Append this MEX to result.
4. Remove the first k elements from arr. Return the lexicographically largest possible result array.

Definitions

• MEX: Smallest non-negative integer missing from a set.
  • MEX({1,2,3}) = 0
  • MEX({0,1,2,4,5}) = 3
• Lexicographically larger:
  • At the first differing position, larger value wins.
  • If one array is a prefix of another, the longer array is larger.

Example

n = 4 arr = [0,1,1,0] k = 2 => MEX({0,1}) = 2 arr = [1,0] result = [2] k = 2 => MEX({1,0}) = 2 arr = [] result = [2,2]

Constraints

• 1 <= n <= 100