CF1268C K Integers

You are given a permutation $ p_1, p_2, \ldots, 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,\ldots, k $ , in other words in the end there should be an integer $ i $ , $ 1 \leq i \leq n-k+1 $ such that $ p_i = 1, p_{i+1} = 2, \ldots, 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,\ldots,k $ appear in the permutation. You need to find $ f(1), f(2), \ldots, f(n) $ .

The first line of input contains one integer $ n $ ( $ 1 \leq n \leq 200\,000 $ ): the number of elements in the permutation. The next line of input contains $ n $ integers $ p_1, p_2, \ldots, p_n $ : given permutation ( $ 1 \leq p_i \leq n $ ).

Print $ n $ integers, the minimum number of moves that you need to make a subsegment with values $ 1,2,\ldots,k $ appear in the permutation, for $ k=1, 2, \ldots, n $ .