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: Accepted)

def p(x, y, n):
  #print('p({},{},{})'.format(x,y,n))
  if x == 0:
    #print('return 0')
    return 0
  count = 0
  if x == y:
    if x <= n:
      count += 1

  i = 0
  flag = True
  while flag:
    for j in range(10**i):
      if (x * 10**(i+1) + y + j *10) <= n:
        #print(': ' + str(x * 10**(i+1) + y + j))
        count+=1
      else:
        flag = False
        break
    i += 1
  #print('return {}'.format(count))
  return count

n = int(input())

#print(p(1, 2, 111))
c = 0
for NF in range(1, 10):
  for NL in range(0, 10):
    #print('({}, {}= {})'.format(NF, NL, p(NF, NL, n)))
    
    c +=  p(NF, NL, n) * p(NL, NF, n)
print(c)