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 <bits/stdc++.h>	
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define pb push_back
#define mp make_pair
#define F first
#define S second
#define ld long double
#define pii pair <int, int>
#define sz(a) (int)(a.size()) 
#define resize(v) v.resize(unique(all(v)) - v.begin()); 
#define all(a) a.begin(), a.end()
#define forit(it, s) for(__typeof(s.begin()) it = s.begin(); it != s.end(); it ++)

// random_device rd; mt19937 g(rd());    
                                        	
using namespace std;
using namespace __gnu_pbds;
 
void Fast_Read_Out()
{
    ios_base::sync_with_stdio(0);
    cin.tie(), cout.tie();
}
 
void Random()
{
    unsigned int seed;                                                                        
    asm("rdtsc" : "=A" (seed));
    srand(seed);        
}
 
unsigned int Time()
{
     unsigned int time = clock() / 1000.00;                           
     return time;
}

template <typename T> using ordered_set = tree <T, null_type, less <T>, rb_tree_tag, tree_order_statistics_node_update>; 
 
const int mod = (int)1e9 + 7;
 
vector <int> v;

pair <int, int> Calc(int a)
{
	int first = 0, second = 0;
	v.clear();			
	while(a)
	{
		v.pb(a % 10);
		a /= 10;
	}
	second = v[0], first = v.back();
	return mp(first, second);
}

long long res;
vector <int> what;
int d[101][101];

int main ()
{
	#ifdef JUDGE
		freopen("input.txt", "r", stdin);
	#endif		
	Fast_Read_Out();
	Random();   
	int n;
	cin >> n;
	for(int a = 1; a <= n; a++)
	{
		pair <int, int> cur = Calc(a);
		d[cur.F][cur.S]++;
	}
	for(int i = 0; i < 10; i++)
		for(int j = 0; j < 10; j++)
			res += d[i][j] * d[j][i];
	cout << res;
}