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 Ruby (2.3.3) (judge verdict: Wrong Answer)

n = gets.chomp.to_i
ans = 0

memo = {}
1.upto(9) do |i|
  1.upto(9) do |u|
    tmp = 0
    if u == i
      1.upto(7) do |m|
        tmp += 1 if (u.to_s * m).to_i <= n
      end
    end
    if (u.to_s + i.to_s).to_i <= n
      tmp += 1
    end
    0.upto(999) do |t|
      if (u.to_s + t.to_s + i.to_s).to_i <= n
        tmp += 1
      end
    end
    memo[i.to_s + u.to_s] = tmp
  end
end

n.downto(1) do |i|
  if i < 10
    ans += 1
    next
  end

  f = i.to_s.split('').first
  l = i.to_s.split('').last
  next if l == '0'
  ans += memo[f.to_s + l.to_s]
end
p ans