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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.NoSuchElementException;

public class Main{
	static FastScanner sc = new FastScanner();
	static PrintWriter out = new PrintWriter(System.out);
	//static String S;
	static int n;
	//static int m;
	
	public static void main(String[] args) {
		n = sc.nextInt();
	
		long cnt = 0;
		for (int i=1; i<=n; i++) {
			if (i%10==0)
				continue;
			
			cnt+=count(top(i),bottom(i));	
		}
		
		out.println(cnt);
		out.flush();
	}
	static long count (int t, int b) {
		long cnt = 0;
		
		if (t==b)
			cnt++;
	
		
		if (b*10+t>n)
			return cnt;
		
		else if (b*100+t>n) 
			cnt++;
		
		else if (b*1000+t>n) {
			long now = b*100+t;
			cnt+=2;
			
			for (int i=0; i<9; i++) {
				now+=10;
				if (now<=n)
					cnt++;
				else
					break;
			}
		}
		
		else if (b*10000+t>n) {
			long now = b*1000+t;
			cnt+=12;
			
			for (int i=0; i<99; i++) {
				now+=10;
				if (now<=n)
					cnt++;
				else
					break;
			}	
		}
		
		else if (b*100000+t>n) {
			long now = b*10000+t;
			cnt+=112;
			for (int i=0; i<999; i++) {
				now+=10;
				if (now<=n)
					cnt++;
				else
					break;
			}	
		}
		else {
			long now = b*100000+t;
			cnt+=1112;
			for (int i=0; i<9999; i++) {
				now+=10;
				if (now<=n)
					cnt++;
				else
					break;
			}	
		}
		return cnt;
	}
	
	
	static int top (int n) {
		while (n>=10)
			n/=10;
		return n;
	}
	
	static int bottom (int n) {
		return n%10;
	}
	
		static class FastScanner {
		    private final InputStream in = System.in;
		    private final byte[] buffer = new byte[1024];
		    private int ptr = 0;
		    private int buflen = 0;

		    private boolean hasNextByte() {
		      if (ptr < buflen) {
		        return true;
		      } else {
		        ptr = 0;
		        try {
		          buflen = in.read(buffer);
		        } catch (IOException e) {
		          e.printStackTrace();
		        }
		        if (buflen <= 0) {
		          return false;
		        }
		      }
		      return true;
		    }

		    private int readByte() {
		      if (hasNextByte()) return buffer[ptr++];
		      else return -1;
		    }

		    private static boolean isPrintableChar(int c) {
		      return 33 <= c && c <= 126;
		    }

		    private void skipUnprintable() {
		      while (hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++;
		    }

		    public boolean hasNext() {
		      skipUnprintable();
		      return hasNextByte();
		    }

		    public String next() {
		      if (!hasNext()) throw new NoSuchElementException();
		      StringBuilder sb = new StringBuilder();
		      int b = readByte();
		      while (isPrintableChar(b)) {
		        sb.appendCodePoint(b);
		        b = readByte();
		      }
		      return sb.toString();
		    }

		    public long nextLong() {
		      if (!hasNext()) throw new NoSuchElementException();
		      long n = 0;
		      boolean minus = false;
		      int b = readByte();
		      if (b == '-') {
		        minus = true;
		        b = readByte();
		      }
		      if (b < '0' || '9' < b) {
		        throw new NumberFormatException();
		      }
		      while (true) {
		        if ('0' <= b && b <= '9') {
		          n *= 10;
		          n += b - '0';
		        } else if (b == -1 || !isPrintableChar(b)) {
		          return minus ? -n : n;
		        } else {
		          throw new NumberFormatException();
		        }
		        b = readByte();
		      }
		    }

		    public int nextInt() {
		      return (int) nextLong();
		    }

		    public int[] nextIntArray(int N, boolean oneBased) {
		      if (oneBased) {
		        int[] array = new int[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      } else {
		        int[] array = new int[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextInt();
		        }
		        return array;
		      }
		    }

		    public long[] nextLongArray(int N, boolean oneBased) {
		      if (oneBased) {
		        long[] array = new long[N + 1];
		        for (int i = 1; i <= N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      } else {
		        long[] array = new long[N];
		        for (int i = 0; i < N; i++) {
		          array[i] = sc.nextLong();
		        }
		        return array;
		      }
		    }
		  }

		}