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 (2.4.0) (judge verdict: Wrong Answer)

n = int(input())
x = n // 10
basenum = x * x + 8
addnum = 0
# print("{0} {1}".format(x* 10 + 1, n))
hassame = False
for i in range(x * 10 + 1, n + 1):
    # print(i)
    for j in range(1, n + 1):
        # print(j)
        if str(i)[0] == str(j)[-1] and str(i)[-1] == str(j)[0]:
            addnum += 1
            if i == j:
                hassame = True
            # print("{0},{1}".format(i, j))
res = basenum + addnum * 2
if hassame:
    res -= 1
# print("n={0}, x={1}, basenum={2}, addnum={3} res ={4}".format(n,x,basenum,addnum,res))
print(res)