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: Accepted)

n = gets.to_i

if n < 10
  puts n
  exit
end

if n == 10
  puts 9
  exit
end

ans = 9
add = 3
head = ''

(11..n).each do |i|
  is = i.to_s
  if head && is[0] != head
    add = 3    
  end
  head = is[0]  
  next if is[-1] == '0'

  d = is.size

  if is[0] == is[-1]
    # puts add
    ans += ("2" * (d-2)).to_i
    ans += add
    add += 2
  elsif i > is.reverse.to_i
    ans += ("2" * (d-1)).to_i
  else
    ans += ("2" * (d-2)).to_i
  end
  # if is[0] == is[-1]
  #   # puts add
  #   ans += add
  #   add += 2
  # end
end
puts ans

# list = []
# (1..n).each do |i|
#   is = i.to_s
#   (1..n).each do |j|
#     js = j.to_s
#     if is[0] == js[-1] && is[-1] == js[0]
#       list << [i, j]
#     end
#   end
# end

# # puts list.inspect

# puts list.size