Problem Description

Happybob has $n$ numbers on the ground. The $i$-th number is denoted as $a_i$. Happybob is studying how to delete all of these numbers. Before he starts all operations, he has one chance to rearrange these numbers in any order. Then he will delete numbers in the following way:

• Happybob has a deletion index $h$ (initially $h=1$). He will set a new variable $H$ with value $a_h$, and then for every positive integer $i$ satisfying $h\le i<k$, he performs $a_i\gets a_{i+1}$ (here $k$ is the current number of remaining numbers on the ground), and deletes the number $a_k$. After that, he sets $h$ to $H$.

• If after any operation, $h$ is strictly greater than the current number of remaining numbers on the ground, then he will not be able to delete any more numbers.

Of course, with this deletion method, it may be impossible to delete all numbers. So he now asks you: what is the maximum number of numbers he can delete?

Input Format

The first line contains a positive integer $t$, the number of test cases.

For each test case:

The first line contains a positive integer $n$, the size of $a$.

The second line contains $n$ positive integers, representing the elements in $a$.

Output Format

Output $t$ lines. Each line contains a positive integer, the answer for the corresponding test case.

2
3
1 2 3
4
114 514 1919 810

3
1

Hint

Sample Explanation

For the first test case, happybob can sort the array $a$ as $[2, 3, 1]$. The deletion process is as follows:

There are no numbers left on the ground, meaning a total of $3$ numbers were deleted.

For the second test case, it can be proven that no matter how you rearrange $a$, you can only delete one number.

Constraints

This problem has multiple test cases.

For $100\%$ of the testdata, it is guaranteed that $1 \le t,n,\sum n\le 5 \times 10^5$, $1\le a_i\le 10^9$. Here $\sum n$ is the sum of $n$ over all test cases.

Translated by ChatGPT 5