4-adjacent

AtCoder

IDarc080_a

Time2000ms

Memory256MB

Difficulty—

We have a sequence of length $N$, $a = (a_1, a_2, ..., a_N)$. Each $a_i$ is a positive integer. Snuke's objective is to permute the element in $a$ so that the following condition is satisfied: * For each $1 ≤ i ≤ N - 1$, the product of $a_i$ and $a_{i + 1}$ is a multiple of $4$. Determine whether Snuke can achieve his objective. ## Constraints * $2 ≤ N ≤ 10^5$ * $a_i$ is an integer. * $1 ≤ a_i ≤ 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

3
1 10 100

Output #1

Yes

One solution is $(1, 100, 10)$.

Input #2

4
1 2 3 4

Output #2

No

It is impossible to permute $a$ so that the condition is satisfied.

Input #3

3
1 4 1

Output #3

Yes

The condition is already satisfied initially.

Input #4

2
1 1

Output #4

No

Input #5

6
2 7 1 8 2 8

Output #5

Yes

API Response (JSON)

{
  "problem": {
    "name": "4-adjacent",
    "description": {
      "content": "We have a sequence of length $N$, $a = (a_1, a_2, ..., a_N)$. Each $a_i$ is a positive integer. Snuke's objective is to permute the element in $a$ so that the following condition is satisfied: *   Fo",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc080_a"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a sequence of length $N$, $a = (a_1, a_2, ..., a_N)$. Each $a_i$ is a positive integer.\nSnuke's objective is to permute the element in $a$ so that the following condition is satisfied:\n\n*   Fo...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments