Sorting By Multiplication
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).
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.
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.
3
5
1 1 2 2 2
6
5 4 3 2 5 1
3
1 2 3
3
2
0
Note
In the first test case, we can perform the operations as follows:
- $l = 2$, $r = 4$, $x = 3$;
- $l = 4$, $r = 4$, $x = 2$;
- $l = 5$, $r = 5$, $x = 10$.
In the second test case, we can perform one operation as follows:
- $l = 1$, $r = 4$, $x = -2$;
- $l = 6$, $r = 6$, $x = 1337$.
In the third test case, the array $a$ is already sorted.