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)

# -*- coding: utf-8 -*-

N = int(input())
ans = 0
if N < 10:
    ans = N
elif N < 100:
    for i in range(N+1):
        if i != 0: 
            if i < 10:
                ans += 1
            elif str(i)[-1] == str(i)[0]:
                ans += 3
            elif str(i)[-1] != '0' and int( str(i)[-1] + str(i)[0] ) <= N:
                ans += 1
else:
    for i in range(N+1):
        if i != 0:
            if i < 10:
                ans += 1
            else:
                if str(i)[-1] == str(i)[0]:
                    ans += ((len(str(i))-1)*2)
            
                ans += 1
                for j in range( len(str(N))-2 ):
                    for k in range(10):
                        if int( str(i)[-1] + j*str(k) + str(i)[0] ) <= N:
                            ans += 1
                   
print(ans)