Make M

AtCoder

IDarc161_a

Time2000ms

Memory256MB

Difficulty—

Let $N$ be a positive **odd** number. A sequence of integers of length $N$, $S = (S_1, S_2, \dots, S_N)$, is said to be **M-type** if "for each even number $i = 2, 4, \dots, N - 1$, it holds that $S_{i-1} < S_i$ and $S_i > S_{i+1}$". You are given a sequence of positive integers of length $N$, $A = (A_1, A_2, \dots, A_N)$. Determine if it is possible to rearrange $A$ to be M-type. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $N$ is an **odd** number. * $1 \leq A_i \leq 10^9 \ \ (1 \leq i \leq N)$ ## Input The input is given from Standard Input in the following format: $N$ $A_1 \ A_2 \ \dots \ A_N$ [samples]

Samples

Input #1

5
1 2 3 4 5

Output #1

Yes

The given sequence is $A = (1, 2, 3, 4, 5)$. After rearranging it, for example, to $B = (4, 5, 1, 3, 2)$,

*   for $i = 2$, it holds that $B_1 = 4 < 5 = B_2$ and $B_2 = 5 > 1 = B_3$;
*   for $i = 4$, it holds that $B_3 = 1 < 3 = B_4$ and $B_4 = 3 > 2 = B_5$.

Therefore, this sequence $B$ is M-type, and the answer is `Yes`.

Input #2

5
1 6 1 6 1

Output #2

Yes

The given sequence $A$ itself is M-type.

Input #3

5
1 6 6 6 1

Output #3

No

It is impossible to rearrange it to be M-type.

API Response (JSON)

{
  "problem": {
    "name": "Make M",
    "description": {
      "content": "Let $N$ be a positive **odd** number. A sequence of integers of length $N$, $S = (S_1, S_2, \\dots, S_N)$, is said to be **M-type** if \"for each even number $i = 2, 4, \\dots, N - 1$, it holds that $S_{",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc161_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let $N$ be a positive **odd** number. A sequence of integers of length $N$, $S = (S_1, S_2, \\dots, S_N)$, is said to be **M-type** if \"for each even number $i = 2, 4, \\dots, N - 1$, it holds that $S_{...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments