311278: CF1959F. 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).

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

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 $b$.