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<map>
#include<iostream>
using namespace std;
#define df 0
#define rep(i,n) for(int i=0;i<(n);i++)
#define repa(i,a,n) for(int i=(a);i<(n);i++)
typedef long int li;

auto p(int x){
  int s=x,t=x%10;
  while(x){
    s=x;
    x/=10;
  }
  return make_pair(s,t);
}

int main(){
  if(df) printf("*debug mode*\n");
  int n; cin >>n;
  map<pair<int,int>,int> mp;
  rep(i,n){
    int x=i+1;
    mp[p(x)]++;
  }
  li ans=0;
  repa(i,1,10){
    li temp=mp[pair<int,int>(i,i)];
    ans+=temp*temp;
  }
  repa(i,1,9){
    repa(j,i+1,10){
      li t1=mp[pair<int,int>(i,j)];
      li t2=mp[pair<int,int>(j,i)];
      ans+=t1*t2*2;
    }
  }
  cout << ans;
}

/// confirm df==0 ///