Sorting By Multiplication

2000ms

262144K

Description:

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).

Input:

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 $$$2 \cdot 10^5$$$.

Output:

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

Sample Input:

3
5
1 1 2 2 2
6
5 4 3 2 5 1
3
1 2 3

Sample Output:

3
2
0

Note:

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.

Informação

Provedor Codeforces

Código CF1861D