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: Time Limit Exceeded)

N = STDIN.gets.chomp.to_i

c = []

(N+1).times do |n|
  i = n.to_s.split('')[0].to_i
  j = n.to_s.split('')[-1].to_i

  c[i] = [] if c[i].nil?
  c[i][j] = 0 if c[i][j].nil?

  # n の先頭の桁の数はi、末尾はj
  c[i][j] += 1
end

ans = 0
10.times do |i|
  10.times do |j|
    next if i == 0 or j == 0
    next if c[i].nil? or c[j].nil?
    # puts "------ i:#{i} j:#{j} ----------"
    # c[i][j] : 先頭 i, 末尾j
    # c[j][i] : 先頭 j, 末尾i
    ans += c[i][j] * c[j][i] unless c[i][j].nil? or c[j][i].nil?
  end
end
puts ans