## GUPTA MECHANICAL

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# [Solution] Sending a Sequence Over the Network Codeforces Solution

E. Sending a Sequence Over the Network
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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 $a=\left[1,2,3,1,2,3\right]$. Suppose it was split into segments as follows: $\left[1\right]+\left[2,3,1\right]+\left[2,3\right]$. Then we could have the following sequences:

• $b=\left[1,1,3,2,3,1,2,3,2\right]$,
• $b=\left[1,1,3,2,3,1,2,2,3\right]$,
• $b=\left[1,1,2,3,1,3,2,2,3\right]$,
• $b=\left[1,1,2,3,1,3,2,3,2\right]$.

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 $b$?

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 yEsyesYes and YES will be recognized as positive response).