B. Seating in a Bus
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

In Berland, a bus consists of a row of $$$n$$$ seats numbered from $$$1$$$ to $$$n$$$. Passengers are advised to always board the bus following these rules:

  • If there are no occupied seats in the bus, a passenger can sit in any free seat;
  • Otherwise, a passenger should sit in any free seat that has at least one occupied neighboring seat. In other words, a passenger can sit in a seat with index $$$i$$$ ($$$1 \le i \le n$$$) only if at least one of the seats with indices $$$i-1$$$ or $$$i+1$$$ is occupied.

Today, $$$n$$$ passengers boarded the bus. The array $$$a$$$ chronologically records the seat numbers they occupied. That is, $$$a_1$$$ contains the seat number where the first passenger sat, $$$a_2$$$ — the seat number where the second passenger sat, and so on.

You know the contents of the array $$$a$$$. Determine whether all passengers followed the recommendations.

For example, if $$$n = 5$$$, and $$$a$$$ = [$$$5, 4, 2, 1, 3$$$], then the recommendations were not followed, as the $$$3$$$-rd passenger sat in seat number $$$2$$$, while the neighboring seats with numbers $$$1$$$ and $$$3$$$ were free.

Input

The first line of input contains a single integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The following describes the input test cases.

The first line of each test case contains exactly one integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the number of seats in the bus and the number of passengers who boarded the bus.

The second line of each test case contains $$$n$$$ distinct integers $$$a_i$$$ ($$$1 \le a_i \le n$$$) — the seats that the passengers occupied in chronological order.

It is guaranteed that the sum of $$$n$$$ values across all test cases does not exceed $$$2 \cdot 10^5$$$, and that no passenger sits in an already occupied seat.

Output

For each test case, output on a separate line:

  • "YES", if all passengers followed the recommendations;
  • "NO" otherwise.

You may output the answer in any case (for example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as a positive answer).

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

The first test case is explained in the problem statement.