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: Wrong Answer)

#include <bits/stdc++.h>
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define all(x) (x).begin(),(x).end()
#define INF 10000000
using ll = long long ;
ll gcd(ll a, ll b) {
  if(b == 0) return a;
  return gcd(b, a % b);
}
ll lcm(ll a,ll b){
    ll g = gcd(a,b);
    return a / g * b;
}
template< int id > struct CompTupleBy
{
  template<class T> 
  bool operator()( const T& a, const T& b ) const {
    return std::get<id>(a) < std::get<id>(b);
  }
};

using namespace std;

int main(){
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll n;
    cin >> n;
    if (n<=10){
        cout << n << endl;
    }else if(n<=20){
        cout << 12 << endl;
    }else if(n<=30){
        cout << 17 << endl;
    }else if(n<=40){
        cout << 24 << endl;
    }else if(n<=50){
        cout << 33 << endl;
    }else if(n<=60){
        cout << 44 << endl;
    }else if(n<=70){
        cout << 57 << endl;
    }else if(n<=80){
        cout << 72 << endl;
    }else if(n<=90){
        cout << 89 << endl;
    }else if(n<=100){
        cout << 108 << endl;
    }else{
        ll tmp = n*n;
        tmp /= 100;
        cout << tmp+8 << endl;
    }
        
}