CF1741E Sending a Sequence Over the Network

The sequence $ a $ is sent over the network as follows: 1. 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); 2. for each segment, its length is written next to it, either to the left of it or to the right of it; 3. 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 $ ?

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: - 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).

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 $ .