Amidst skyscrapers in the bustling metropolis of Metro Manila, the newest Noiph mall in the Philippines has just been completed! The construction manager, Penchick, ordered a state-of-the-art monument to be built with $n$ pillars.

The heights of the monument's pillars can be represented as an array $h$ of $n$ positive integers, where $h_i$ represents the height of the $i$-th pillar for all $i$ between $1$ and $n$.

Penchick wants the heights of the pillars to be in non-decreasing order, i.e. $h_i \le h_{i + 1}$ for all $i$ between $1$ and $n - 1$. However, due to confusion, the monument was built such that the heights of the pillars are in non-increasing order instead, i.e. $h_i \ge h_{i + 1}$ for all $i$ between $1$ and $n - 1$.

Luckily, Penchick can modify the monument and do the following operation on the pillars as many times as necessary:

• Modify the height of a pillar to any positive integer. Formally, choose an index $1\le i\le n$ and a positive integer $x$. Then, assign $h_i := x$.

Help Penchick determine the minimum number of operations needed to make the heights of the monument's pillars non-decreasing.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 1000$). The description of the test cases follows.

The first line of each test case contains a single integer $n$ ($1 \leq n \leq 50$) — the number of pillars.

The second line of each test case contains $n$ integers $h_1, h_2, \ldots, h_n$ ($1 \le h_i \le n$ and $h_i\ge h_{i+1}$) — the height of the pillars.

Please take note that the given array $h$ is non-increasing.

Note that there are no constraints on the sum of $n$ over all test cases.

Output

For each test case, output a single integer representing the minimum number of operations needed to make the heights of the pillars non-decreasing.

Note

In the first test case, the initial heights of pillars are $h = [5, 4, 3, 2, 1]$.

• In the first operation, Penchick changes the height of pillar $1$ to $h_1 := 2$.
• In the second operation, he changes the height of pillar $2$ to $h_2 := 2$.
• In the third operation, he changes the height of pillar $4$ to $h_4 := 4$.
• In the fourth operation, he changes the height of pillar $5$ to $h_5 := 4$.

After the operation, the heights of the pillars are $h = [2, 2, 3, 4, 4]$, which is non-decreasing. It can be proven that it is not possible for Penchick to make the heights of the pillars non-decreasing in fewer than $4$ operations.

In the second test case, Penchick can make the heights of the pillars non-decreasing by modifying the height of pillar $3$ to $h_3 := 2$.

In the third test case, the heights of pillars are already non-decreasing, so no operations are required.

Samples

3
5
5 4 3 2 1
3
2 2 1
1
1

4
1
0