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 Python (3.8.2) (judge verdict: Wrong Answer)

n = int(input())
cou = 0
for i in range(1,n+1):
  i = str(i)
  if i[0]!="0" and i[-1]!="0":
    if int(i[0])>int(i[-1]):
      cou +=  (9**(len(i)-1)-1)//8
    elif int(i[0])<int(i[-1]):
      cou += (9**(len(i)-2)-1)//8
  #print(i,cou)

cou *= 2
    
l = [0 for i in range(9)]
for i in range(1,n+1):
  i = str(i)
  if i[0]==i[-1]:
    l[int(i[0])-1] += 1
l1 = [i*i for i in l]
print(sum(l1)+cou)