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)

def main():
    N = int(input())
    r = 0
    for i in range(1, min(10, N+1)):
        r += 1
        if N >= int(str(i) * 2):
            r += 1
        else:
            continue
        j = 1
        while True:
            if int(str(i) + '9' * j  + str(i)) > N:
                r += complex(i, i, j, N)
                break
            else:
                r += 10 ** j
                j += 1
    if N < 10:
        return r
    for i in range(11, N+1):
        if i % 10 == 0:
            continue
        t = int(str(i)[0])
        b = int(str(i)[-1])
        if t == b:
            r += 1
        if N >= int(str(b) + str(t)):
            r += 1
        else:
            continue
        j = 1
        while True:
            if int(str(b) + '9' * j + str(t)) > N:
                r += complex(b, t, j, N)
                break
            else:
                r += 10 ** j
                j += 1
    return r
def complex(b, t, j, N):
    if int(str(b) + '0' * j + str(t)) > N:
        return 0
    N_m = int(str(N)[1:-1])
    if t >= int(str(N)[-1]):
        return (N_m)
    return N_m - 1
print(main())