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 Python (3.4.3) (judge verdict: Wrong Answer)

def check(A,N):
    if N<10:
        return int(N==A)
    res=0
    if A<10:
        a=b=str(A)
        res+=1
    else:
        a,b=str(A)[0],str(A)[-1]
    if b==0:return 0
    n=1
    while N>10**n:
        if n==1:
            res+=(int(b+a)<=N)
        else:
            res+=sum([(int(b+str(i)+a)<=N) for i in list(range(10**(n-1)))])
        n+=1
    return res

N=int(input())
res=0
for i in range(N):
    res+=check(i+1,N)
print(res)