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: Accepted)

n = int(input())
ans = 0
for i in range(1,n+1):
    if str(i)[-1] == "0":
        pass
    elif i < 10:
        ans += 1
    elif i <= 100:
        if str(i)[0] == str(i)[-1]:
            ans += 3
        elif int(str(i)[0]) > int(str(i)[1]):
            ans += 2
    elif i <= 1000:
        if str(i)[0] == str(i)[-1]:
            ans += (int(str(i)[1])+3)*2-1
        elif int(str(i)[0]) > int(str(i)[-1]):
            ans += 22
        elif int(str(i)[0]) < int(str(i)[-1]):
            ans += 2
    elif i <= 10000:
        if str(i)[0] == str(i)[-1]:
            ans += (int(str(i)[1:3]) + 13)*2-1
        elif int(str(i)[0]) > int(str(i)[-1]):
            ans += 222
        elif int(str(i)[0]) < int(str(i)[-1]):
            ans += 22
    elif i <= 100000:
        if str(i)[0] == str(i)[-1]:
            ans += (int(str(i)[1:4]) + 113)*2-1
        elif int(str(i)[0]) > int(str(i)[-1]):
            ans += 2222
        elif int(str(i)[0]) < int(str(i)[-1]):
            ans += 222
    elif i <= 1000000:
        if str(i)[0] == str(i)[-1]:
            ans += (int(str(i)[1:5]) + 1113)*2-1
        elif int(str(i)[0]) > int(str(i)[-1]):
            ans += 22222
        elif int(str(i)[0]) < int(str(i)[-1]):
            ans += 2222
print(ans)