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)

require 'pp'

def get_nums
  gets.split.map(&:to_i)
end

def init_matrix(row_num, row_length, default = nil)
  Array.new(row_num).map { Array.new(row_length, default) }
end

top_and_bottoms = Array.new(10).map {Array.new(10, 0)}

inp = gets.chomp
n = inp.to_i
digits = inp.size

res = 0
1.upto(n) do |i|
  i_s = i.to_s
  top_digit = i_s[0].to_i
  end_digit = i_s[-1].to_i
  top_and_bottoms[top_digit][end_digit] += 1
  # top_and_bottoms[end_digit][top_digit] += 1
end

res = 0

0.upto(9) do |i|
  i_eq_j = false
  0.upto(9) do |j|
    next if i_eq_j && i == j
    # puts "Ok" if i == j && i == 1
    i_eq_j = true if i == j
    # p [i, j, top_and_bottoms[i], top_and_bottoms[i][j], top_  and_bottoms[j][i]]
    # p [i, j] if top_and_bottoms[i][j] * top_and_bottoms[j][i] != 0

    res += top_and_bottoms[i][j] * top_and_bottoms[j][i]
  end
end

pp top_and_bottoms

puts res