Equal LIS

AtCoder

IDagc052_d

Time2000ms

Memory256MB

Difficulty—

You are given a permutation $P_1, P_2, \dots, P_N$ of integers from $1$ to $N$. Is it possible to split it into $2$ subsequences, which have equal length of the Longest Increasing Subsequence? Formally speaking, your goal is to get two integer sequences $a$ and $b$ such that: * Both $a$ and $b$ are subsequences of $P$. * Each integer $i=1,2,\cdots,N$ appears in exactly one of $a$ and $b$. * (The length of a longest increasing subsequence of $a$) $=$ (The length of a longest increasing subsequence of $b$) Determine if the objective is achievable. You will be given $T$ test cases. Solve each of them. ## Constraints * $1 \le T \le 2 \cdot 10^5$ * $1 \le N \le 2 \cdot 10^5$ * $P_1, P_2, \dots, P_N$ is a permutation of integers from $1$ to $N$. * The sum of $N$ over all test cases doesn't exceed $2 \cdot 10^5$. ## Input Input is given from Standard Input in the following format. The first line of input is as follows: $T$ Then, $T$ test cases follow, each of which is in the following format: $N$ $P_1$ $P_2$ $\dots$ $P_N$ [samples]

Samples

Input #1

5
1
1
2
2 1
3
1 2 3
5
1 3 5 2 4
6
2 3 4 5 6 1

Output #1

NO
YES
NO
YES
NO

$[1, 3, 5, 2, 4]$ can be split into $[1, 5]$ and $[3, 2, 4]$, both have $LIS$ of length 2.
It can be shown that there is no way to split $[2, 3, 4, 5, 6, 1]$ into $2$ subsequences with an equal length of $LIS$.

API Response (JSON)

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      "content": "You are given a permutation $P_1, P_2, \\dots, P_N$ of integers from $1$ to $N$. Is it possible to split it into $2$ subsequences, which have equal length of the Longest Increasing Subsequence?\nFormall...",
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