You are given an array (a) containing (n) integers. In one operation, you can choose some elements from this array and remove them. However, the elements you choose must meet one of the following conditions: either all chosen elements are equal; or there are no two equal chosen elements. Note that if you choose only (1) element to remove, it automatically meets these conditions. For example, if (a = \{1, 2, 1, 1, 3\}), some of the possible elements you can remove in one operation are: the (1)-st element; the (1)-st and the (3)-rd element; the (1)-st, the (3)-rd and the (4)-th element; the (3)-rd and the (4)-th element; the (2)-nd, the (4)-th and the (5)-th element; and many others. However, you cannot choose the (2)-nd, the (3)-rd and the (4)-th element because the (2)-nd element is not equal to the (4)-th, but the (3)-rd element is equal to the (4)-th. For each (x) from (0) to (n - 1), you have to calculate the minimum number of operations required to decrease the size of the array to exactly (x). The first line contains one integer (t) ((1 \le t \le 10^4)) — the number of test cases. Each test case consists of two lines: the first line contains one integer (n) ((1 \le n \le 3 \cdot 10^5)) — the size of the array; the second line contains (n) integers (a_1, a_2, \dots, a_n) ((1 \le a_i \le n)) — the array itself. Additional constraint on the input: the sum of (n) over all test cases does not exceed (3 \cdot 10^5). For each test case, print (n) integers (c_0, c_1, \dots, c_{n-1}), where (c_i) is the minimum number of operations required to reduce the size of the array to exactly (i). In the first example, the answer can be obtained as follows: (c_{0} = 3): remove (a_{8}, a_{9}, a_{10}, a_{11}); then remove (a_{1}, a_{2}, a_{3}, a_{4}); then remove (a_{5}, a_{6}, a_{7}); (c_{1} = 3):