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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

n = int(input())

ans = 0
for i in range(1,10) :
  for j in range(i,10) :
    c_a = 0
    c_b = 0
    for k in range(1,n+1) :
      if int(str(k)[0]) == i and int(str(k)[-1]) == j :
        c_a += 1
      if int(str(k)[0]) == j and int(str(k)[-1]) == i :
        c_b += 1
    if i == j :
      ans += c_a*c_b
    else :
      ans += c_a*c_b*2
print(ans)