Codeforces Round 826 (Div. 3) |
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Finished |
The sequence $$$a$$$ is sent over the network as follows:
For example, we needed to send the sequence $$$a = [1, 2, 3, 1, 2, 3]$$$. Suppose it was split into segments as follows: $$$[\color{red}{1}] + [\color{blue}{2, 3, 1}] + [\color{green}{2, 3}]$$$. Then we could have the following sequences:
If a different segmentation had been used, the sent sequence might have been different.
The sequence $$$b$$$ is given. Could the sequence $$$b$$$ be sent over the network? In other words, is there such a sequence $$$a$$$ that converting $$$a$$$ to send it over the network could result in a sequence $$$b$$$?
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 $$$2 \cdot 10^5$$$.
For each test case print on a separate line:
You can output YES and NO in any case (for example, strings yEs, yes, Yes and YES will be recognized as positive response).
791 1 2 3 1 3 2 2 3512 1 2 7 565 7 8 9 10 344 8 6 223 1104 6 2 1 9 4 9 3 4 211
YES YES YES NO YES YES NO
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 $$$b$$$.
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