You are given an array $a$ of $n$ elements $a_1, a_2, \ldots, a_n$.

You can perform the following operation any number (possibly $0$) of times:

• Choose two integers $i$ and $j$, where $1 \le i, j \le n$, and assign $a_i := a_j$.

Find the minimum number of operations required to make the array $a$ satisfy the condition:

• For every pairwise distinct triplet of indices $(x, y, z)$ ($1 \le x, y, z \le n$, $x \ne y$, $y \ne z$, $x \ne z$), there exists a non-degenerate triangle with side lengths $a_x$, $a_y$ and $a_z$, i.e. $a_x + a_y \gt a_z$, $a_y + a_z \gt a_x$ and $a_z + a_x \gt a_y$.

Input

Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($3 \le n \le 2 \cdot 10^5$) — the number of elements in the array $a$.

The second line of each test case contains $n$ integers $a_1, a_2, \ldots, a_n$ ($1 \le a_i \le 10^9$) — the elements of the array $a$.

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

Output

For each test case, output a single integer — the minimum number of operations required.

Note

In the first test case, one of the possible series of operations would be:

• Assign $a_1 := a_4 = 4$. The array will become $[4, 2, 3, 4, 5, 6, 7]$.
• Assign $a_2 := a_5 = 5$. The array will become $[4, 5, 3, 4, 5, 6, 7]$.
• Assign $a_7 := a_1 = 4$. The array will become $[4, 5, 3, 4, 5, 6, 4]$.

It can be proven that any triplet of elements with pairwise distinct indices in the final array forms a non-degenerate triangle, and there is no possible answer using less than $3$ operations.

In the second test case, we can assign $a_1 := a_2 = 3$ to make the array $a = [3, 3, 2]$.

In the third test case, since $3$, $4$ and $5$ are valid side lengths of a triangle, we don't need to perform any operation to the array.