1269_E. K Integers
Problem Description
You are given a permutation p_1, p_2, …, p_n.
In one move you can swap two adjacent values.
You want to perform a minimum number of moves, such that in the end there will exist a subsegment 1,2,…, k, in other words in the end there should be an integer i, 1 ≤ i ≤ n-k+1 such that p_i = 1, p_{i+1} = 2, …, p_{i+k-1}=k.
Let f(k) be the minimum number of moves that you need to make a subsegment with values 1,2,…,k appear in the permutation.
You need to find f(1), f(2), …, f(n).
Input
The first line of input contains one integer n (1 ≤ n ≤ 200 000): the number of elements in the permutation.
The next line of input contains n integers p_1, p_2, …, p_n: given permutation (1 ≤ p_i ≤ n).
Output
Print n integers, the minimum number of moves that you need to make a subsegment with values 1,2,…,k appear in the permutation, for k=1, 2, …, n.
Examples
Input
5 5 4 3 2 1
Output
0 1 3 6 10
Input
3 1 2 3
Output
0 0 0
Contest Information
- Contest ID: 1269
- Problem Index: E
- Points: 1500.0
- Rating: 2300
- Tags: binary search, data structures
- Time Limit: {'seconds': 3, 'nanos': 0} seconds
- Memory Limit: 256000000 bytes
Task
Solve this competitive programming problem. Provide a complete solution that handles all the given constraints and edge cases.