Increasing Triples

AtCoder

IDarc123_b

Time2000ms

Memory256MB

Difficulty—

Given are three sequences of $N$ integers each: $A = (A_1, \ldots, A_N),\,B = (B_1, \ldots, B_N),\,C = (C_1, \ldots, C_N)$. You can permute each of these sequences in any way you like. Find the maximum possible number of indices $i$ such that $A_i < B_i < C_i$ after permuting them. ## Constraints * $1\leq N\leq 10^5$ * $1\leq A_i, B_i, C_i\leq 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ $B_1$ $B_2$ $\ldots$ $B_N$ $C_1$ $C_2$ $\ldots$ $C_N$ [samples]

Samples

Input #1

5
9 6 14 1 8
2 10 3 12 11
15 13 5 7 4

Output #1

3

We should permute them as follows:

*   $A = (1,6,8,9,14)$,
*   $B = (3,2,10,12,11)$,
*   $C = (4,7,15,13,5)$.

Then, we will have three indices $i$ ($i = 1, 3, 4$) such that $A_i < B_i < C_i$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

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  "problem": {
    "name": "Increasing Triples",
    "description": {
      "content": "Given are three sequences of $N$ integers each: $A = (A_1, \\ldots, A_N),\\,B = (B_1, \\ldots, B_N),\\,C = (C_1, \\ldots, C_N)$. You can permute each of these sequences in any way you like. Find the maximu",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
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    "is_sync": true,
    "sync_url": null,
    "sign": "arc123_b"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are three sequences of $N$ integers each: $A = (A_1, \\ldots, A_N),\\,B = (B_1, \\ldots, B_N),\\,C = (C_1, \\ldots, C_N)$.\nYou can permute each of these sequences in any way you like. Find the maximu...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments