B'Sam is a kindergartener, and there are n children in his group. He decided to create a team with some of his children to play "brawl:go 2". Sam has n power-ups, the i -th has type a_i . A child 's strength is equal to the number of different types among power-ups he has. For a team of size k , Sam will distribute all n power-ups to k children in such a way that each of the k children receives at least one power-up, and each power-up is given to someone. For each integer k from 1 to n , find the minimum sum of strengths of a team of k children Sam can get. Each test contains multiple test cases. The first line contains a single integer t ( 1 <= t <= 3 cdot 10^5 ) -- the number of test cases. Description of the test cases follows. The first line of each test case contains a single integer n ( 1 <= n <= 3 cdot 10^5 ). The second line contains n integers a_1, a_2, ldots, a_n ( 1 <= a_i <= 10^9 ) -- types of Sam 's power-ups. It is guaranteed that the sum of n over all test cases does not exceed 3 cdot 10^5 . For every test case print n integers. The k -th integer should be equal to the minimum sum of strengths of children in the team of size k that Sam can get. One of the ways to give power-ups to minimise the sum of strengths in the first test case: One of the ways to give power-ups to minimise the sum of strengths in the second test case: '...