Problem:
Score : 400 points

Problem Statement

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

Output

Print the answer.

Sample Input 1

25

Sample 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).

Sample Input 2

1

Sample Output 2

1

Sample Input 3

100

Sample Output 3

108

Sample Input 4

2020

Sample Output 4

40812

Sample Input 5

200000

Sample Output 5

400000008

Solution in JavaScript (node.js v5.12) (judge verdict: Accepted)

'use strict'


const pair = (x) => {
  const a = x%10 // 末尾の一桁
  let b = 0

  // 一桁目の取得
  while(x) {
    b = x
    x = Math.floor(x/10)
  }

  return [a, b]
}

function Main(input) {
  input = input.trim()
  const N = parseInt(input)
  let c = 0
  let map = {}

  // 組み合わせのマップを作成する
  for(let i = 1; i <= N; ++i) {
    let p = pair(i)
    if(!map[p]) map[p] = 0
    map[p]++
  }

  // 組み合わせマップから答えを算出する
  for(let i = 1; i <= N; ++i) {
    let p = pair(i)
    let q = [p[1], p[0]]
    if(map[q]) {
      c += map[q]
    }
  }

  console.log(c)
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));