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: Accepted)

import sys
def I(): return int(sys.stdin.readline())
def LI(): return [int(x) for x in sys.stdin.readline().split()]

def calc(a,b,n):
    ret = 0
    if a==b and a<=n:
        ret += 1
    if a*10+b <= n:
        ret += 1
    for i in range(2,7):
        if a*(10**i)+b>n:
            break
        if a*(10**i)+(10**i)-10+b<=n:
            ret += 10**(i-1)
            continue
        tmp = n
        while(tmp%10!=b):
            tmp -= 1
        tmp -= a*(10**i)
        tmp //= 10
        tmp += 1
        ret += tmp
    return ret

def main():
    N = I()
    ans = 0
    for A in range(1,10):
        for B in range(1,10):
            ans += calc(A,B,N) * calc(B,A,N)
    print(ans)

if __name__ == "__main__":
    main()