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 = input()
M = int(N[0])
L = len(N)
cond_l = [[],[],[],[],[],[],[],[],[]]
for i in range(1,10):
  for j in range(1,10):
    t = 0
    if i == j:
      t += 1
    if i < M:
      for k in range(2, L+1):
        t += 10 ** (k - 2)
    elif i > M:
      for k in range(2, L):
        t += 10 ** (k - 2)
    else:
      for k in range(2, L):
        t += 10 ** (k - 2)
      if L >= 2:
        t_2 = 1
        for k in range(1, L-2):
          t_2 *= int(N[k]) + 1
        if L >= 3 and j <= int(N[-1]):
          t_2 *= int(N[L-2]) + 1
        elif L >= 3:
          t_2 *= int(N[L-2])
        t += t_2
    cond_l[i-1].append(t)
ans = 0
for i in range(9):
  ans += cond_l[i][i] ** 2
for i in range(8):
  for j in range(i+1, 9):
    ans += cond_l[i][j] * cond_l[j][i] * 2
print(ans)