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())

l = [0 for _ in range(81)]
for k in range(1, n + 1):
    i = int(str(k)[0])
    j = int(str(k)[-1])
    if i != 0 and j != 0:
        idx = 9 * (i - 1) + (j - 1)
        l[idx] += 1
    # print("k = " + str(k))
    # print(i, j, idx)
ans = 0
for i in range(1, 10):
    for j in range(1, 10):
        idx = 9 * (i - 1) + (j - 1)
        idx2 = 9 * (j - 1) + (i - 1)
        ans += l[idx] * l[idx2]
        # print("(" + str(i) + str(j) + ") * (" + str(j) + str(i) + ") = " + str(l[idx]) + "*" +  str(l[idx2]) + " = " +  str(l[idx] * l[idx2]))
# print(l)
print(ans)