#D1943. Omkar and Medians
Omkar and Medians
Omkar and Medians
Uh oh! Ray lost his array yet again! However, Omkar might be able to help because he thinks he has found the OmkArray of Ray's array. The OmkArray of an array a with elements a_1, a_2, …, a_{2k-1}, is the array b with elements b_1, b_2, …, b_{k} such that b_i is equal to the median of a_1, a_2, …, a_{2i-1} for all i. Omkar has found an array b of size n (1 ≤ n ≤ 2 ⋅ 10^5, -10^9 ≤ b_i ≤ 10^9). Given this array b, Ray wants to test Omkar's claim and see if b actually is an OmkArray of some array a. Can you help Ray?
The median of a set of numbers a_1, a_2, …, a_{2i-1} is the number c_{i} where c_{1}, c_{2}, …, c_{2i-1} represents a_1, a_2, …, a_{2i-1} sorted in nondecreasing order.
Input
Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.
The first line of each test case contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array b.
The second line contains n integers b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9) — the elements of b.
It is guaranteed the sum of n across all test cases does not exceed 2 ⋅ 10^5.
Output
For each test case, output one line containing YES if there exists an array a such that b_i is the median of a_1, a_2, ..., a_{2i-1} for all i, and NO otherwise. The case of letters in YES and NO do not matter (so yEs and No will also be accepted).
Examples
Input
5 4 6 2 1 3 1 4 5 4 -8 5 6 -7 2 3 3 4 2 1 2 3
Output
NO YES NO YES YES
Input
5 8 -8 2 -6 -5 -4 3 3 2 7 1 1 3 1 0 -2 -1 7 6 12 8 6 2 6 10 6 5 1 2 3 6 7 5 1 3 4 3 0
Output
NO YES NO NO NO
Note
In the second case of the first sample, the array [4] will generate an OmkArray of [4], as the median of the first element is 4.
In the fourth case of the first sample, the array [3, 2, 5] will generate an OmkArray of [3, 3], as the median of 3 is 3 and the median of 2, 3, 5 is 3.
In the fifth case of the first sample, the array [2, 1, 0, 3, 4, 4, 3] will generate an OmkArray of [2, 1, 2, 3] as
- the median of 2 is 2
- the median of 0, 1, 2 is 1
- the median of 0, 1, 2, 3, 4 is 2
- and the median of 0, 1, 2, 3, 3, 4, 4 is 3.
In the second case of the second sample, the array [1, 0, 4, 3, 5, -2, -2, -2, -4, -3, -4, -1, 5] will generate an OmkArray of [1, 1, 3, 1, 0, -2, -1], as
- the median of 1 is 1
- the median of 0, 1, 4 is 1
- the median of 0, 1, 3, 4, 5 is 3
- the median of -2, -2, 0, 1, 3, 4, 5 is 1
- the median of -4, -2, -2, -2, 0, 1, 3, 4, 5 is 0
- the median of -4, -4, -3, -2, -2, -2, 0, 1, 3, 4, 5 is -2
- and the median of -4, -4, -3, -2, -2, -2, -1, 0, 1, 3, 4, 5, 5 is -1
For all cases where the answer is NO, it can be proven that it is impossible to find an array a such that b is the OmkArray of a.
inputFormat
Input
Each test contains multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases. Description of the test cases follows.
The first line of each test case contains an integer n (1 ≤ n ≤ 2 ⋅ 10^5) — the length of the array b.
The second line contains n integers b_1, b_2, …, b_n (-10^9 ≤ b_i ≤ 10^9) — the elements of b.
It is guaranteed the sum of n across all test cases does not exceed 2 ⋅ 10^5.
outputFormat
Output
For each test case, output one line containing YES if there exists an array a such that b_i is the median of a_1, a_2, ..., a_{2i-1} for all i, and NO otherwise. The case of letters in YES and NO do not matter (so yEs and No will also be accepted).
Examples
Input
5 4 6 2 1 3 1 4 5 4 -8 5 6 -7 2 3 3 4 2 1 2 3
Output
NO YES NO YES YES
Input
5 8 -8 2 -6 -5 -4 3 3 2 7 1 1 3 1 0 -2 -1 7 6 12 8 6 2 6 10 6 5 1 2 3 6 7 5 1 3 4 3 0
Output
NO YES NO NO NO
Note
In the second case of the first sample, the array [4] will generate an OmkArray of [4], as the median of the first element is 4.
In the fourth case of the first sample, the array [3, 2, 5] will generate an OmkArray of [3, 3], as the median of 3 is 3 and the median of 2, 3, 5 is 3.
In the fifth case of the first sample, the array [2, 1, 0, 3, 4, 4, 3] will generate an OmkArray of [2, 1, 2, 3] as
- the median of 2 is 2
- the median of 0, 1, 2 is 1
- the median of 0, 1, 2, 3, 4 is 2
- and the median of 0, 1, 2, 3, 3, 4, 4 is 3.
In the second case of the second sample, the array [1, 0, 4, 3, 5, -2, -2, -2, -4, -3, -4, -1, 5] will generate an OmkArray of [1, 1, 3, 1, 0, -2, -1], as
- the median of 1 is 1
- the median of 0, 1, 4 is 1
- the median of 0, 1, 3, 4, 5 is 3
- the median of -2, -2, 0, 1, 3, 4, 5 is 1
- the median of -4, -2, -2, -2, 0, 1, 3, 4, 5 is 0
- the median of -4, -4, -3, -2, -2, -2, 0, 1, 3, 4, 5 is -2
- and the median of -4, -4, -3, -2, -2, -2, -1, 0, 1, 3, 4, 5, 5 is -1
For all cases where the answer is NO, it can be proven that it is impossible to find an array a such that b is the OmkArray of a.
样例
5
8
-8 2 -6 -5 -4 3 3 2
7
1 1 3 1 0 -2 -1
7
6 12 8 6 2 6 10
6
5 1 2 3 6 7
5
1 3 4 3 0
NO
YES
NO
NO
NO