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)

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import array
from bisect import *
from collections import *
import fractions
import heapq
from itertools import *
import math
import random
import re
import string
import sys

N = int(input())

def brute(N):
    ans = []
    for a in range(1, N + 1):
        for b in range(1, N + 1):
            a2 = str(a)
            b2 = str(b)
            if a2[0] == b2[-1] and a2[-1] == b2[0]:
                ans.append((a, b))

    return ans

def faster(N):
    arr = defaultdict(list)
    c = Counter()
    for n in range(1, N + 1):
        s = str(n)
        first = s[0]
        last = s[-1]
        arr[first + last].append(n)
        c[first + last] += 1

    ans = 0
    for key in c:
        key2 = key[-1] + key[0]
        ans += c[key] * c[key2]

    for n in range(11, 100, 11):
        s = str(n)
        ans -= len(arr[n]) * len(arr[n])

    return ans

print(faster(N))

# for n in range(1, 1000):
#     b = len(brute(n))
#     f = faster(n)
#     if b != f:
#         print("error!")
#         print(b, f)
#         sys.exit(0)