Greedy Takahashi 2

AtCoder

IDarc211_e

Time2000ms

Memory256MB

Difficulty—

You are given a positive integer $N$ and a permutation $P$ of $(1,2,\dots,N)$. When there is a tree with $N$ vertices numbered $1,2,\dots,N$, Snuke and Takahashi move according to the following rules: * Snuke specifies a permutation $Q$ of $(1,2,\dots,N)$ such that the sequence returned by Takahashi, when following the rules below, is lexicographically maximum. * Takahashi, who is at vertex $1$ of the tree, first receives $Q$ from Snuke and initializes an integer sequence $R$ with the length-$1$ sequence $(Q_1)$. Then, he moves $N-1$ times as follows, and returns the final $R$: * Visit the vertex $i$ with the smallest $Q_i$ among vertices that are adjacent to a previously visited vertex but have not yet been visited (it can be proved that there is always exactly one such vertex). Then, append $Q_i$ to the end of $R$. Here, vertex $1$ is considered to have been visited initially. Determine whether there exists a tree such that Takahashi returns $P$. You are given $T$ test cases; solve each of them. ## Constraints * $1 \le T \le 10^5$ * $1 \le N \le 2 \times 10^5$ * $P$ is a permutation of $(1,2,\dots,N)$. * The sum of $N$ over all test cases is at most $2 \times 10^5$. * All input values are integers. ## Input The input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\text{case}_2$ $\vdots$ $\text{case}_T$ Each test case is given in the following format: $N$ $P_1$ $P_2$ $\ldots$ $P_N$ [samples]

Samples

Input #1

3
4
4 2 3 1
4
4 1 3 2
11
11 8 9 6 7 10 3 4 5 1 2

Output #1

Yes
No
Yes

For the first test case, a tree with four vertices having edges between vertices $1$\-$2$, $1$\-$3$, and $2$\-$4$ satisfies the conditions.
If Snuke specifies $Q=(4,3,2,1)$, Takahashi visits vertices $1,3,2,4$ in this order and returns $R=(4,2,3,1)$. No matter what $Q$ Snuke specifies, it is impossible to make Takahashi return a sequence lexicographically larger than $(4,2,3,1)$, so the sequence that ends up being returned is $(4,2,3,1)$.
For the second test case, it can be proved that there is no tree satisfying the conditions.

API Response (JSON)

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      "content": "You are given a positive integer $N$ and a permutation $P$ of $(1,2,\\dots,N)$. When there is a tree with $N$ vertices numbered $1,2,\\dots,N$, Snuke and Takahashi move according to the following rules:",
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "You are given a positive integer $N$ and a permutation $P$ of $(1,2,\\dots,N)$.\nWhen there is a tree with $N$ vertices numbered $1,2,\\dots,N$, Snuke and Takahashi move according to the following rules:...",
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