Sending a Sequence Over the Network

Description:

Input:

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

Each test case consists of two lines.

The first line of the test case contains an integer $$$n$$$ ($$$1 \le n \le 2 \cdot 10^5$$$) — the size of the sequence $$$b$$$.

The second line of test case contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$1 \le b_i \le 10^9$$$) — the sequence $$$b$$$ itself.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

Output:

For each test case print on a separate line:

• YES if sequence $$$b$$$ could be sent over the network, that is, if sequence $$$b$$$ could be obtained from some sequence $$$a$$$ to send $$$a$$$ over the network.
• NO otherwise.

You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as positive response).

Sample Input:

7
9
1 1 2 3 1 3 2 2 3
5
12 1 2 7 5
6
5 7 8 9 10 3
4
4 8 6 2
2
3 1
10
4 6 2 1 9 4 9 3 4 2
1
1

Sample Output:

YES
YES
YES
NO
YES
YES
NO

Note:

In the first case, the sequence $$$b$$$ could be obtained from the sequence $$$a = [1, 2, 3, 1, 2, 3]$$$ with the following partition: $$$[\color{red}{1}] + [\color{blue}{2, 3, 1}] + [\color{green}{2, 3}]$$$. The sequence $$$b$$$: $$$[\color{red}{1}, 1, \color{blue}{2, 3, 1}, 3, 2, \color{green}{2, 3}]$$$.

In the second case, the sequence $$$b$$$ could be obtained from the sequence $$$a = [12, 7, 5]$$$ with the following partition: $$$[\color{red}{12}] + [\color{green}{7, 5}]$$$. The sequence $$$b$$$: $$$[\color{red}{12}, 1, 2, \color{green}{7, 5}]$$$.

In the third case, the sequence $$$b$$$ could be obtained from the sequence $$$a = [7, 8, 9, 10, 3]$$$ with the following partition: $$$[\color{red}{7, 8, 9, 10, 3}]$$$. The sequence $$$b$$$: $$$[5, \color{red}{7, 8, 9, 10, 3}]$$$.

In the fourth case, there is no sequence $$$a$$$ such that changing $$$a$$$ for transmission over the network could produce a sequence $$$b$$$.