A sequence of \(n\) integers \(a_1, a_2, \dots, a_n\) is called a peak, if and only if there exists exactly one integer \(k\) such that \(1 < k < n\), and \(a_i < a_{i+1}\) for all \(1 \le i < k\), and \(a_{i-1} > a_i\) for all \(k < i \le n\).
Given an integer sequence, please tell us if it's a peak or not.
Input
There are multiple test cases. The first line of the input contains an integer \(T\), indicating the number of test cases. For each test case:
The first line contains an integer \(n\) (\(3 \le n \le 10^5\)), indicating the length of the sequence.
The second line contains \(n\) integers \(a_1, a_2, \dots, a_n\) (\(1 \le a_i \le 2 \times 10^9\)), indicating the integer sequence.
It's guaranteed that the sum of \(n\) in all test cases won't exceed \(10^6\).
Output
For each test case output one line. If the given integer sequence is a peak, output "Yes" (without quotes), otherwise output "No" (without quotes).
Sample Input
7
5
1 5 7 3 2
5
1 2 1 2 1
4
1 2 3 4
4
4 3 2 1
3
1 2 1
3
2 1 2
5
1 2 3 1 2
Sample Output
Yes
No
No
No
Yes
No
No