E. Exquisite Array
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

We call an array of numbers $$$k$$$-exquisite if it has at least two elements and any two adjacent numbers differ by at least $$$k$$$.

You are given a permutation$$$^{\text{∗}}$$$ $$$p$$$ of length $$$n$$$. For each $$$k$$$ from $$$1$$$ to $$$n - 1$$$, find the number of $$$k$$$-exquisite subarrays$$$^{\text{†}}$$$.

$$$^{\text{∗}}$$$A permutation of length $$$n$$$ is an array that contains each integer from $$$1$$$ to $$$n$$$ exactly once, in any order.

$$$^{\text{†}}$$$A subarray of an array is a sequence of one or more consecutive elements of the array.

Input

Each test consists of several test cases. The first line contains a single integer $$$t$$$ $$$(1 \le t \le 25000)$$$ — the number of test cases. The descriptions of the test cases follow.

In the first line of each test case, an integer $$$n$$$ is given — the length of the permutation $$$(2 \le n \le 10^5)$$$.

In the second line of each test case, $$$n$$$ integers $$$p_i$$$ are given — the elements of the permutation $$$(1 \le p_i \le n)$$$. It is guaranteed that $$$p_i$$$ are distinct.

It is guaranteed that the sum of $$$n$$$ across all test cases does not exceed $$$2 \cdot 10^5$$$.

Output

For each test case, output the number of $$$k$$$-exquisite subarrays for all $$$k$$$ from $$$1$$$ to $$$n - 1$$$.

Example
Input
3
5
5 1 4 2 3
3
3 2 1
4
3 1 2 4
Output
10 6 3 1 
3 0 
6 2 0