You want to build some obstacle courses. You are given a 0-indexed integer array obstacles of length n, where obstacles[i] describes the height of the ith obstacle.
For every index i between 0 and n - 1 (inclusive), find the length of the longest obstacle course in obstacles such that:
- You choose any number of obstacles between
0andiinclusive. - You must include the
ithobstacle in the course. - You must put the chosen obstacles in the same order as they appear in
obstacles. - Every obstacle (except the first) is taller than or the same height as the obstacle immediately before it.
Return an array ans of length n, where ans[i] is the length of the longest obstacle course for index i as described above.
Example 1:
Input: obstacles = [1,2,3,2] Output: [1,2,3,3] Explanation: The longest valid obstacle course at each position is: - i = 0: [1], [1] has length 1. - i = 1: [1,2], [1,2] has length 2. - i = 2: [1,2,3], [1,2,3] has length 3. - i = 3: [1,2,3,2], [1,2,2] has length 3.
Example 2:
Input: obstacles = [2,2,1] Output: [1,2,1] Explanation: The longest valid obstacle course at each position is: - i = 0: [2], [2] has length 1. - i = 1: [2,2], [2,2] has length 2. - i = 2: [2,2,1], [1] has length 1.
Example 3:
Input: obstacles = [3,1,5,6,4,2] Output: [1,1,2,3,2,2] Explanation: The longest valid obstacle course at each position is: - i = 0: [3], [3] has length 1. - i = 1: [3,1], [1] has length 1. - i = 2: [3,1,5], [3,5] has length 2. [1,5] is also valid. - i = 3: [3,1,5,6], [3,5,6] has length 3. [1,5,6] is also valid. - i = 4: [3,1,5,6,4], [3,4] has length 2. [1,4] is also valid. - i = 5: [3,1,5,6,4,2], [1,2] has length 2.
Constraints:
n == obstacles.length1 <= n <= 1051 <= obstacles[i] <= 107