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)

import math

n = int(input())
mp = [[0 for _ in range(10)] for _ in range(10)]

for i in range(1, n + 1):
    mp[int(str(i)[0])][int(str(i)[-1])] += 1

sm = 0
for i in range(10):
    for j in range(10):
        sm += mp[i][j] * mp[j][i]

print(sm)

# c = 0
# for i in range(1, n):
#     for j in range(1, n):
#         si, sj = str(i), str(j)
#         if si[0] == sj[-1] and si[-1] == sj[0]:
#             c += 1