Ball Coloring

AtCoder

IDarc073_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ bags, each containing two white balls. The $i$\-th box contains two balls with integers $x_i$ and $y_i$ written on them, respectively. For each of these bags, you will paint one of the balls red, and paint the other blue. Afterwards, the $2N$ balls will be classified according to color. Then, we will define the following: * $R_{max}$: the maximum integer written on a ball painted in red * $R_{min}$: the minimum integer written on a ball painted in red * $B_{max}$: the maximum integer written on a ball painted in blue * $B_{min}$: the minimum integer written on a ball painted in blue Find the minimum possible value of $(R_{max} - R_{min}) \times (B_{max} - B_{min})$. ## Constraints * $1 ≤ N ≤ 200,000$ * $1 ≤ x_i, y_i ≤ 10^9$ ## Input Input is given from Standard Input in the following format: $N$ $x_1$ $y_1$ $x_2$ $y_2$ : $x_N$ $y_N$ [samples]

Samples

Input #1

Output #1

15

The optimal solution is to paint the balls with $x_1$, $x_2$, $y_3$ red, and paint the balls with $y_1$, $y_2$, $x_3$ blue.

Input #2

Output #2

Input #3

2
1 1
1000000000 1000000000

Output #3

999999998000000001

API Response (JSON)

{
  "problem": {
    "name": "Ball Coloring",
    "description": {
      "content": "There are $N$ bags, each containing two white balls. The $i$\\-th box contains two balls with integers $x_i$ and $y_i$ written on them, respectively. For each of these bags, you will paint one of the b",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc073_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ bags, each containing two white balls. The $i$\\-th box contains two balls with integers $x_i$ and $y_i$ written on them, respectively.\nFor each of these bags, you will paint one of the b...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments