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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

n = int(input())
m = len(str(n))
ans = 0



for i in range(n + 1):
    A = str(i)
    first = A[0]
    end = A[-1]

    if end == '0':
        continue
    if first == end:
        ans += 1


    if m >= 3:
        for j in range(m - 2):
            ans += 10 ** (j)
    mini = int(end + '0' * (m - 2) + first)
    maxi = int(end + '9' * (m - 2) + first)
    # print(mini, maxi)
    if n < mini:
        continue
    elif mini <= n <= maxi:
        # print(i, mini, maxi)
        if int(str(n)[-1]) > int(first):
            ans += int(str(n)[1:-1])
            # print('a')
        else:
            ans += int(str(n)[1:-1])
            # print('a')
    else:
        ans += (10 ** (m - 2))

print(ans)