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 (7.3.0) (judge verdict: Accepted)

n = int(input())

if n < 10:
    print(n)
    quit()

count = [[0] * 10 for _ in range(10)]
for i in range(1, 10):
    count[i][i] = 1

d = 1
for i in range(10, n + 1):
    if i % (d * 10)== 0:
        d *= 10
    h = i // d
    f = i % 10
    count[h][f] += 1

ans = 0
for i in range(10):
    for j in range(10):
        ans += count[i][j] * count[j][i]
print(ans)