Min Diff Sum

AtCoder

IDarc147_c

Time2000ms

Memory256MB

Difficulty—

$N$ people, numbered $1,2,\ldots ,N$, are going to stand on the number line. Let's denote by $x_i$ the coordinate the Person $i$ stands at. Then, $x_i$ should be an integer satisfying $L_i \leq x_i \leq R_i$. Multiple people can occupy the same coordinate. We define the **dissatisfaction level** as the following formula: > $\displaystyle\sum_{i=1}^{N-1}\sum_{j=i+1}^{N}|x_j-x_i|$ Find the minimum possible value of the dissatisfaction level. ## Constraints * $2 \leq N \leq 3 \times 10^5$ * $1 \leq L_i \leq R_i \leq 10^7 \,(1 \leq i \leq N)$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $L_1$ $R_1$ $L_2$ $R_2$ $\vdots$ $L_N$ $R_N$ [samples]

Samples

Input #1

Output #1

4

If we let $x_1=3,x_2=4,x_3=5$, we get the dissatisfaction level of $4$. We cannot make it $3$ or less, so the answer is $4$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Min Diff Sum",
    "description": {
      "content": "$N$ people, numbered $1,2,\\ldots ,N$, are going to stand on the number line. Let's denote by $x_i$ the coordinate the Person $i$ stands at. Then, $x_i$ should be an integer satisfying $L_i \\leq x_i \\l",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc147_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "$N$ people, numbered $1,2,\\ldots ,N$, are going to stand on the number line. Let's denote by $x_i$ the coordinate the Person $i$ stands at. Then, $x_i$ should be an integer satisfying $L_i \\leq x_i \\l...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments