Minimum or Maximum

 From a hidden array $A$ of length $N$, Stack constructs an array $B$ of length $N$ such that:

• For all $i$ $(1 \leq i \leq N)$, $B_i=\max(A_1,A_2,\ldots,A_i)$ or $B_i=\min(A_1,A_2,\ldots,A_i)$.

For the given array $B$ of length $N$, Stack wants you to check whether a possible array $A$ exists or not.

Input Format

• The first line of input contains a single integer $T$, denoting the number of test cases. The description of $T$ test cases follow.
• The first line of each test case contains an integer $N$ - the length of the array $B$.
• The second line of each test case contains $N$ space-separated integers $B_1,B_2,\ldots,B_N$ representing the array $B$.

Output Format

For each test case, output in a single line YES if $A$ exists, otherwise print NO.

You may print each character of the string in uppercase or lowercase (for example, the strings YES, yEs, yes, and yeS will all be treated as identical).

Constraints

• $1 \leq T \leq 10^5$
• $1 \leq N \leq 10^5$
• $1 \leq B_i \leq 10^5$
• Sum of $N$ over all test cases does not exceed $10^5$.

Sample Input 1 

3
1
343
4
1 1 2 3
3
1 3 2

Sample Output 1 

YES
YES
NO

Explanation

Test case $1$: The only possible array is $A=[343]$.

Test case $2$: One possible array is $A=[1,1,2,3]$. In this case $B_i = max(A_1, A_2, \ldots, A_i)$ satisfies for all $1 \le i \le 4$.

Test case $3$: It can be proven that there exists no $A$ from which we can obtain the given array $B$.

Sample Input 2 

2
5
1 1 1 1 1 
5
1 2 1 2 1

Sample Output 2 

YES
YES

Explanation

Test case $1$: The only possible array is $A=[1,1,1,1,1]$.

Test case $2$: One possible array is $A=[1,2,1,1,1]$. In this case,

• $B_1=A_1$
• $B_2=\max(A_1,A_2)$
• $B_3=\min(A_1,A_2,A_3)$
• $B_4=\max(A_1,A_2,A_3,A_4)$
• $B_5=\min(A_1,A_2,A_3,A_4,A_5)$