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)

# https://atcoder.jp/contests/abc152/tasks/abc152_d

s = gets.chomp
N = s.to_i
l = s.size

css = Array.new(10) { Array.new(10, 0) }

1.upto(9) do |i|
  1.upto(9) do |j|
    ix = s[0].to_i
    jx = s[-1].to_i
    c = 0
    c += (i <= N ? 1 : 0) if i == j
    (l - 2).times { |k| c += 10**k }
    if l >= 2
      if i < ix
        c += 10**(l - 2)
      elsif i == ix
        c += ('0' + s[1..-2]).to_i
        c += 1 if j <= jx
      end
    end
    css[i][j] = c
  end
end

# p css

ans = 0
1.upto(9) do |i|
  1.upto(9) do |j|
    ans += css[i][j] * css[j][i]
  end
end

puts ans