A13605. Make It Good

You are given an array $a$ consisting of $n$ integers. You have to find the length of the smallest (shortest) prefix of elements you need to erase from $a$ to make it a good array. Recall that the prefix of the array $a=[a_1, a_2, \dots, a_n]$ is a subarray consisting several first elements: the prefix of the array $a$ of length $k$ is the array $[a_1, a_2, \dots, a_k]$ ( $0 \le k \le n$ ).

The array $b$ of length $m$ is called good, if you can obtain a non-decreasing array $c$ ( $c_1 \le c_2 \le \dots \le c_{m}$ ) from it, repeating the following operation $m$ times (initially, $c$ is empty):

- select either the first or the last element of $b$ , remove it from $b$ , and append it to the end of the array $c$ .

For example, if we do $4$ operations: take $b_1$ , then $b_{m}$ , then $b_{m-1}$ and at last $b_2$ , then $b$ becomes $[b_3, b_4, \dots, b_{m-3}]$ and $c =[b_1, b_{m}, b_{m-1}, b_2]$ .

Consider the following example: $b = [1, 2, 3, 4, 4, 2, 1]$ . This array is good because we can obtain non-decreasing array $c$ from it by the following sequence of operations:

1. take the first element of $b$ , so $b = [2, 3, 4, 4, 2, 1]$ , $c = [1]$ ;
2. take the last element of $b$ , so $b = [2, 3, 4, 4, 2]$ , $c = [1, 1]$ ;
3. take the last element of $b$ , so $b = [2, 3, 4, 4]$ , $c = [1, 1, 2]$ ;
4. take the first element of $b$ , so $b = [3, 4, 4]$ , $c = [1, 1, 2, 2]$ ;
5. take the first element of $b$ , so $b = [4, 4]$ , $c = [1, 1, 2, 2, 3]$ ;
6. take the last element of $b$ , so $b = [4]$ , $c = [1, 1, 2, 2, 3, 4]$ ;
7. take the only element of $b$ , so $b = []$ , $c = [1, 1, 2, 2, 3, 4, 4]$ — $c$ is non-decreasing.

Note that the array consisting of one element is good.

Print the length of the shortest prefix of $a$ to delete (erase), to make $a$ to be a good array. Note that the required length can be $0$ .

You have to answer $t$ independent test cases.

The first line of the input contains one integer $t$ ( $1 \le t \le 2 \cdot 10^4$ ) — the number of test cases. Then $t$ test cases follow.

The first line of the test case contains one integer $n$ ( $1 \le n \le 2 \cdot 10^5$ ) — the length of $a$ . The second line of the test case contains $n$ integers $a_1, a_2, \dots, a_n$ ( $1 \le a_i \le 2 \cdot 10^5$ ), where $a_i$ is the $i$ -th element of $a$ .

It is guaranteed that the sum of $n$ does not exceed $2 \cdot 10^5$ ( $\sum n \le 2 \cdot 10^5$ ).

For each test case, print the answer: the length of the shortest prefix of elements you need to erase from $a$ to make it a good array.

In the first test case of the example, the array $a$ is already good, so we don't need to erase any prefix.

In the second test case of the example, the initial array $a$ is not good. Let's erase first $4$ elements of $a$ , the result is $[4, 5, 2]$ . The resulting array is good. You can prove that if you erase fewer number of first elements, the result will not be good.