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 (Clang 3.8.0) (judge verdict: Accepted)

#include<unordered_map>
#include<algorithm>
#include<iostream>
#include<string.h>
#include<utility>
#include<stdio.h>
#include<vector>
#include<string>
#include<math.h>
#include<cmath>
#include<queue>
#include<stack>
#include<deque>
#include<map>
#pragma warning(disable:4244)
#define PI 3.1415926536
#pragma GCC optimize(2)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
const ll ll_inf = 9223372036854775807;
const int int_inf = 2147483647;
const short short_inf = 32767;
const char char_inf = 127;
inline ll read() {
	ll c = getchar(), Nig = 1, x = 0;
	while (!isdigit(c) && c != '-')c = getchar();
	if (c == '-')Nig = -1, c = getchar();
	while (isdigit(c))x = ((x << 1) + (x << 3)) + (c ^ '0'), c = getchar();
	return Nig * x;
}
inline void out(ll a)
{
	if (a < 0)putchar('-'), a = -a;
	if (a >= 10)out(a / 10);
	putchar(a % 10 + '0');
}
ll qpow(ll x, ll n, ll mod) {
	ll res = 1;
	while (n > 0) {
		if (n & 1)res = (res * x) % mod;
		x = (x * x) % mod; n >>= 1;
	}
	return res;
}
#define read read()
int save[200][200];
int main()
{
	int n = read;
	for (int i = 1; i <= n; i++)
	{
		int temp = i;
		int len = log10(i);
		int N = pow(10, len);
		int num = temp / N;
		save[num][i % 10]++;
	}
	int ans = 0;
	for (int i = 0; i < 10; i++)
	{
		for (int j = 0; j < 10; j++)
			ans += save[i][j] * save[j][i];
	}
	cout << ans << endl;
}