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)

def calc1(x,y,N): # x != y
    d = len(str(N))
    if d == 1:
        re = 0
    elif d == 2:
        if N >= x*(10**(d-1)) + y:
            re = 1
        else:
            re = 0
    else:
        s_high = str(x) + '9'*(d-2) + str(y)
        s_low = str(x) + '0'*(d-2) + str(y)
        if N >= int(s_high):
            re = int(str('1'*(d - 1)))
        else:
            re = int('1'*(d-2))
            if N >= int(s_low):
                re += (N - int(s_low))//10 + 1
    return re

def calc2(x,y,N): # x == y
    d = len(str(N))
    if d == 1:
        if x <= N:
            re = 1
        else:
            re = 0
    elif d == 2:
        if N >= x*(10**(d-1)) + y:
            re = 2
        else:
            re = 1
    else:
        s_high = str(x) + '9'*(d-2) + str(y)
        s_low = str(x) + '0'*(d-2) + str(y)
        if N >= int(s_high):
            re = int(str('1'*(d - 1))) + 1
        else:
            re = int('1'*(d-2)) + 1
            if N >= int(s_low):
                re += (N - int(s_low))//10 + 1
    return re
N = int(input())
ans = 0
for i in range(1,10):
    for j in range(1,10):
        if i != j:
            ans += calc1(i,j,N)*calc1(j,i,N)
for i in range(1,10):
    ans +=calc2(i,i,N)**2
print(ans)