Handstand 2

AtCoder

IDabc152_d

Time2000ms

Memory256MB

Difficulty—

Given is a positive integer $N$. Find the number of pairs $(A, B)$ of positive integers not greater than $N$ that satisfy the following condition: * When $A$ and $B$ are written in base ten without leading zeros, the last digit of $A$ is equal to the first digit of $B$, and the first digit of $A$ is equal to the last digit of $B$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ [samples]

Samples

Input #1

Output #1

17

The following $17$ pairs satisfy the condition: $(1,1)$, $(1,11)$, $(2,2)$, $(2,22)$, $(3,3)$, $(4,4)$, $(5,5)$, $(6,6)$, $(7,7)$, $(8,8)$, $(9,9)$, $(11,1)$, $(11,11)$, $(12,21)$, $(21,12)$, $(22,2)$, and $(22,22)$.

Input #2

Output #2

Input #3

Output #3

Input #4

Output #4

Input #5

Output #5

400000008

API Response (JSON)

{
  "problem": {
    "name": "Handstand 2",
    "description": {
      "content": "Given is a positive integer $N$.   Find the number of pairs $(A, B)$ of positive integers not greater than $N$ that satisfy the following condition: *   When $A$ and $B$ are written in base ten witho",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc152_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a positive integer $N$.  \nFind the number of pairs $(A, B)$ of positive integers not greater than $N$ that satisfy the following condition:\n\n*   When $A$ and $B$ are written in base ten witho...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments