Colorful Hats

AtCoder

IDagc016_b

Time2000ms

Memory256MB

Difficulty—

There are $N$ cats. We number them from $1$ through $N$. Each of the cats wears a hat. Cat $i$ says: "there are exactly $a_i$ different colors among the $N - 1$ hats worn by the cats except me." Determine whether there exists a sequence of colors of the hats that is consistent with the remarks of the cats. ## Constraints * $2 ≤ N ≤ 10^5$ * $1 ≤ a_i ≤ N-1$ ## Input Input is given from Standard Input in the following format: $N$ $a_1$ $a_2$ $...$ $a_N$ [samples]

Samples

Input #1

3
1 2 2

Output #1

Yes

For example, if cat $1$, $2$ and $3$ wears red, blue and blue hats, respectively, it is consistent with the remarks of the cats.

Input #2

3
1 1 2

Output #2

No

From the remark of cat $1$, we can see that cat $2$ and $3$ wear hats of the same color. Also, from the remark of cat $2$, we can see that cat $1$ and $3$ wear hats of the same color. Therefore, cat $1$ and $2$ wear hats of the same color, which contradicts the remark of cat $3$.

Input #3

5
4 3 4 3 4

Output #3

No

Input #4

3
2 2 2

Output #4

Yes

Input #5

4
2 2 2 2

Output #5

Yes

Input #6

5
3 3 3 3 3

Output #6

No

API Response (JSON)

{
  "problem": {
    "name": "Colorful Hats",
    "description": {
      "content": "There are $N$ cats. We number them from $1$ through $N$. Each of the cats wears a hat. Cat $i$ says: \"there are exactly $a_i$ different colors among the $N - 1$ hats worn by the cats except me.\" Deter",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc016_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ cats. We number them from $1$ through $N$.\nEach of the cats wears a hat. Cat $i$ says: \"there are exactly $a_i$ different colors among the $N - 1$ hats worn by the cats except me.\"\nDeter...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments