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 (3.4.3) (judge verdict: Wrong Answer)

N = int(input())
nstr = str(N)
nlen = len(nstr)
cnt = 0
Nmiddle = 1
for k in range(1,nlen-1):
  Nmiddle *= int(nstr[k])
if nlen == 2:
  Nmiddle = 0
for i in range(1, N+1):
  j = str(i)
  if j[0] == j[-1]:
    cnt += 1
  if nlen - 3 > 0:
    cnt += ((10**(nlen - 2) - 1)/9)
  if N >= int(j[-1] + ('9' * (nlen - 2)) + j[0]):
    cnt += 10**(nlen - 2)
  elif nstr[0] < j[0]:
    continue
  elif nstr[0] == j[0]:
    if nstr[-1] < j[-1]:
      cnt += Nmiddle - 1
    else:
      cnt += Nmiddle
print(cnt)