Equalize the Array

Polycarp was gifted an array a of length n. Polycarp considers an array beautiful if there exists a number C, such that each number in the array occurs either zero or C times. Polycarp wants to remove some elements from the array a to make it beautiful.

For example, if n=6 and a = [1, 3, 2, 1, 4, 2], then the following options are possible to make the array a array beautiful:

• Polycarp removes elements at positions 2 and 5, array a becomes equal to [1, 2, 1, 2];
• Polycarp removes elements at positions 1 and 6, array a becomes equal to [3, 2, 1, 4];
• Polycarp removes elements at positions 1, 2 and 6, array a becomes equal to [2, 1, 4];

Help Polycarp determine the minimum number of elements to remove from the array a to make it beautiful.

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of each test case consists of one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array a.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — array a.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case, output one integer — the minimum number of elements that Polycarp has to remove from the array a to make it beautiful.

Example

Input

3 6 1 3 2 1 4 2 4 100 100 4 100 8 1 2 3 3 3 2 6 6

Output

2 1 2

inputFormat

Input

The first line contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases. Then t test cases follow.

The first line of each test case consists of one integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array a.

The second line of each test case contains n integers a_1, a_2, …, a_n (1 ≤ a_i ≤ 10^9) — array a.

It is guaranteed that the sum of n over all test cases does not exceed 2 ⋅ 10^5.

outputFormat

Output

For each test case, output one integer — the minimum number of elements that Polycarp has to remove from the array a to make it beautiful.

Example

Input

3 6 1 3 2 1 4 2 4 100 100 4 100 8 1 2 3 3 3 2 6 6

Output

2 1 2

样例

3
6
1 3 2 1 4 2
4
100 100 4 100
8
1 2 3 3 3 2 6 6

2
1
2

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