E. Sending a Sequence Over the Networktime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputThe sequence a is sent over the network as follows:  sequence a is split into segments (each element of the sequence belongs to exactly one segment, each segment is a group of consecutive elements of sequence);  for each segment, its length is written next to it, either to the left of it or to the right of it;  the resulting sequence b is sent over the network. 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:   b = [1, \color{red}{1}, 3, \color{blue}{2, 3, 1}, \color{green}{2, 3}, 2],  b = [\color{red}{1}, 1, 3, \color{blue}{2, 3, 1}, 2, \color{green}{2, 3}],  b = [\color{red}{1}, 1, \color{blue}{2, 3, 1}, 3, 2, \color{green}{2, 3}],  b = [\color{red}{1}, 1,\color{blue}{2, 3, 1}, 3, \color{green}{2, 3}, 2]. 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?InputThe 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.OutputFor 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).ExampleInput
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 211Output
YES
YES
YES
NO
YES
YES
NO
NoteIn 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.
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 
['dp', '*1600']