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())
if N <= 10:
    print(1)
else:
    ret = 0
    #diff num
    for i in range(1,10):
      for j in range(i+1,10):
        a = 0
        b = 0
        for k in range(1, 6):
          if i * 10 ** k + j < N:
            a += 10 ** (k - 1)
        for k in range(1, 6):
          if j * 10 ** k + i < N:
            b += 10 ** (k - 1)
            ret += a * b * 2
         #same num
    for i in range(1,10):
      c = 1
      for k in range(1,6):
        if i * 10 ** k + i < N:
           c += 10 ** (k - 1)
      ret += c * c
    print(ret)