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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <fstream>
#include <sstream>
#include <random>
#include <string>
#include <algorithm>
#include <vector>
#include <math.h>
#include <queue>
#include <iostream>
#include <functional>
#include <stdio.h>
#include <string.h>
#include <unordered_map>
#include <set>
#include <iomanip>

#define ll long long
#define mod 1000000007
using namespace std;

int computeFirstDigit(int a) {
    while(a >= 10) {
        a = a/10;
    }
    return a;
}


int main() {

    int n;
    cin>>n;

    int digits[10][10];
    for(int i = 0; i <= 9; i++) {
        for(int j = 0; j <= 9; j++) {
            digits[i][j] = 0;
        }
    }

    for(int i = 1; i <= n; i++) {
        digits[computeFirstDigit(i)][i%10] += 1;
    }

    ll total = 0;
    for(int i = 1; i <= 9; i++) {
        for(int j = 1; j <= 9; j++) {
            if(i == j) {
                total += digits[i][j]*digits[i][j];
            }
            else {
                total += digits[i][j]*digits[j][i];
            }
        }
    }
    cout<<total<<'\n';
    return 0;
}