A16100. Sorting By Multiplication

You are given an array $a$ of length $n$ , consisting of positive integers.

You can perform the following operation on this array any number of times (possibly zero):

- choose three integers $l$ , $r$ and $x$ such that $1 \le l \le r \le n$ , and multiply every $a_i$ such that $l \le i \le r$ by $x$ .

Note that you can choose any integer as $x$ , it doesn't have to be positive.

You have to calculate the minimum number of operations to make the array $a$ sorted in strictly ascending order (i. e. the condition $a_1 < a_2 < \dots < a_n$ must be satisfied).

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

The first line of each test case contains one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the length of the array $a$ .

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

Additional constraint on the input: the sum of $n$ over all test cases does not exceed $2 \cdot 10^5$ .

For each test case, print one integer — the minimum number of operations required to make $a$ sorted in strictly ascending order.

In the first test case, we can perform the operations as follows:

- $l = 2$ , $r = 4$ , $x = 3$ ;
- $l = 4$ , $r = 4$ , $x = 2$ ;
- $l = 5$ , $r = 5$ , $x = 10$ .

After these operations, the array $a$ becomes $[1, 3, 6, 12, 20]$ .In the second test case, we can perform one operation as follows:

- $l = 1$ , $r = 4$ , $x = -2$ ;
- $l = 6$ , $r = 6$ , $x = 1337$ .

After these operations, the array $a$ becomes $[-10, -8, -6, -4, 5, 1337]$ .In the third test case, the array $a$ is already sorted.