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: Time Limit Exceeded)

N = int(input())
t = [[0 for i in range(9)] for _ in range(9)]
ans = 0
for i in range(1, 10):
    for l in range(1, 10):
        for q in range(1, N+1):
            s = 0
            if int(str(q)[0]) == i and int(str(q)[-1]) == l:
                s += 1
            t[i - 1][l - 1] += s
for i in range(1, N+1):
    a = str(i)[0]
    b = str(i)[-1]
    if b == "0":
        continue
    elif a == b:
        ans += t[int(a)-1][int(a)-1]
    else:
        ans += t[int(b)-1][int(a)-1]
print(ans)