Who's a good array? You're a good array! (c)

An array $$$b$$$ is good if there do not exist indices $$$1 \leq i \lt j \leq |b|$$$ such that $$$b_j - b_i = 1$$$.

You are given an integer. array $$$a_1, a_2, \ldots, a_n$$$. Determine the minimum number of elements that need to be removed from the given array so that it becomes a good array.

Input

Each test contains multiple test cases. The first line contains the number of test cases $$$t$$$ ($$$1 \le t \le 6 \cdot 10^4$$$). The description of the test cases follows.

The first line of each test case contains an integer $$$n$$$ ($$$1 \leq n \leq 3 \cdot 10^5$$$) — the number of elements in the array.

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

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$3 \cdot 10^5$$$.

Output

For each test case, print a single integer — the minimum number of elements that need to be removed from the array to make it a good array.

Note

In the first test case, the array is good from the very beginning, so nothing needs to be removed from it.

In the second test case, the optimal solution is to remove the second and fourth elements of the array, which will result in $$$1$$$, $$$3$$$, $$$5$$$ array.

In the third test case, the array is good from the very beginning.

In the fourth test case, the array is good from the very beginning.

In the fifth test case, the optimal solution is to remove the fourth element of the array, which will result in $$$1$$$, $$$7$$$, $$$1$$$, $$$5$$$, $$$7$$$, $$$1$$$ array.

In the sixth test case, one of the optimal solutions is to remove the first and fourth elements of the array, which will result in $$$2$$$, $$$5$$$, $$$5$$$, $$$5$$$ array.

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Examples