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 = input()
L = len(N)
if L == 1:
    print(int(N))
    exit()

def count(c,d):
    if c == int(N[0]):
        if L == 2:
            if d > int(N[-1]):
                n = 0
            else:
                n = 1
        else:
            n = int(N[1:-1]) + 1
            n += sum(10**i for i in range(L-2))
            if d > int(N[-1]):
                n -= 1
    elif c < int(N[0]):
        n = sum(10**i for i in range(L-1))
    else: # c > N[0]
        if L == 2:
            n = 0
        else:
            n = sum(10**i for i in range(L-2))
    if c == d:
        n += 1
    return n

ans = 0
for c in range(1,10):
    for d in range(1,10):
        nA = count(c,d)
        nB = count(d,c)
        if nA * nB > 0:
            print(c,d,nA,nB)
        ans += nA * nB
print(ans)