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: Wrong Answer)

import math
N=int(input())
#A=list(map(int,input().split()))
digit=int(math.log(N,10))+1 
def c_ij(i,j):
  count=0
  if i==0:
    return (0)
  if N<=9:
    if i==j<=N:
      return (1)   
  elif digit == 2:
    if i*10+j<=N:
      count +=1
    if i == j:
      count +=1
  else:
    for a in range(2,digit):
      count += 10**(a-2)
    if i == j:
      count +=1
    if int(str(N)[0])>i:
      count += 10**(digit-2)
    else:  
      calc=N-int(str(i)+'0'*(digit-2)+str(j))
      if calc > 0:
        count += sum([(int(str(calc)[-i-1])+1)*10**(i-1) for i in range(1,min(digit-1, int(math.log(calc,10))+1 ))])
  return (count)


ans=0
for a in range(10):
  for b in range(10):
    ans += c_ij(a,b)*c_ij(b,a)
    #print(a,b,c_ij(a,b),c_ij(b,a))
print(ans)