G. Removal of a Permutationtime limit per test5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given a permutation $$$p$$$ of length $$$n$$$.You can perform operations of two types: mark all positions $$$i$$$ such that $$$1 \le i < n$$$ and $$$p_i < p_{i + 1}$$$, and simultaneously remove the elements at these positions; mark all positions $$$i$$$ such that $$$2 \le i \le n$$$ and $$$p_{i - 1} > p_i$$$, and simultaneously remove the elements at these positions. For each integer from $$$1$$$ to $$$(n-1)$$$, calculate the minimum number of operations required to remove that integer from the permutation.InputThe first line contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.The first line of each test case contains a single integer $$$n$$$ ($$$2 \le n \le 250\,000$$$).The second line of each test case contains $$$n$$$ integers $$$p_1, p_2, \dots, p_n$$$ ($$$1 \le p_i \le n$$$). The array $$$p$$$ is a permutation.Additional constraints on the input: the sum of $$$n$$$ over all test cases does not exceed $$$250\,000$$$.OutputFor each test case, print $$$(n-1)$$$ integers. The $$$i$$$-th of them should be equal to the minimum number of operations required to remove $$$i$$$ from the permutation.ExampleInput544 2 1 321 265 4 1 3 2 675 6 1 3 7 2 453 1 2 5 4Output1 1 2
1
1 1 2 1 3
1 1 1 2 1 2
1 1 2 1