Solve the programming task below in a Python markdown code block.
You have an array $a$ of length $n$. You can exactly once select an integer $len$ between $1$ and $n - 1$ inclusively, and then sort in non-decreasing order the prefix of the array of length $len$ and the suffix of the array of length $n - len$ independently.

For example, if the array is $a = [3, 1, 4, 5, 2]$, and you choose $len = 2$, then after that the array will be equal to $[1, 3, 2, 4, 5]$.

Could it be that after performing this operation, the array will not be sorted in non-decreasing order?


-----Input-----

There are several test cases in the input data. The first line contains a single integer $t$ ($1 \leq t \leq 100$) — the number of test cases. This is followed by the test cases description.

The first line of each test case contains one integer $n$ ($2 \leq n \leq 10^4$) — the length of the array.

The second line of the test case contains a sequence of integers $a_1, a_2, \ldots, a_n$ ($1 \leq a_i \leq 10^9$) — the array elements.

It is guaranteed that the sum of $n$ over all test cases does not exceed $10^4$.


-----Output-----

For each test case of input data, output "YES" (without quotes), if the array may be not sorted in non-decreasing order, output "NO" (without quotes) otherwise. You can output each letter in any case (uppercase or lowercase).


-----Examples-----

Input
3
3
2 2 1
4
3 1 2 1
5
1 2 2 4 4
Output
YES
YES
NO


-----Note-----

In the first test case, it's possible to select $len = 1$, then after operation, the array will not be sorted in non-decreasing order and will be equal to $[2, 1, 2]$.

In the second test case, it's possible to select $len = 3$, then after operation, the array will not be sorted in non-decreasing order and will be equal to $[1, 2, 3, 1]$.

In the third test case, the array will be sorted in non-decreasing order for every possible $len$.