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())
X = ['']
for i in range(1, 6):
    for j in range(10**i):
        X.append(str(j).zfill(i))
cnt = 0
for a in range(1, n+1):
    x = str(a)[0]
    y = str(a)[-1]
    if x == y:
        cnt += 1
    if y == '0':
        continue
    l, r = 0, len(X)
    while r-l > 1:
        c = (l+r)//2
        if int(y+X[c]+x) <= n:
            l = c
        else:
            r = c
    cnt += r
print(cnt)