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())
s=[]
t=[]
for i in range(9):
    s.append([])
for i in range(100):
    t.append([[],[]])
for i in range(1,n+1):
    a=str(i)
    b=max(int(a[0]),int(a[len(a)-1]))
    c=min(int(a[0]),int(a[len(a)-1]))
    if b!=0 and c!=0:
        if b==c:
            s[b-1].append(i)
        elif int(a[0])<int(a[len(a)-1]):
            t[b*9+c][0].append(i)
        else:
            t[b*9+c][1].append(i)
ans=0
for i in range(9):
    x=len(s[i])
    ans+=x**2
for i in range(100):
    x=len(t[i][0])
    y=len(t[i][1])
    ans+=2*x*y
print(ans)