Problem:
Score : 300 points

Problem Statement

2N players are running a competitive table tennis training on N tables numbered from 1 to N.

The training consists of rounds.
In each round, the players form N pairs, one pair per table.
In each pair, competitors play a match against each other.
As a result, one of them wins and the other one loses.

The winner of the match on table X plays on table X-1 in the next round,
except for the winner of the match on table 1 who stays at table 1.

Similarly, the loser of the match on table X plays on table X+1 in the next round,
except for the loser of the match on table N who stays at table N.

Two friends are playing their first round matches on distinct tables A and B.
Let's assume that the friends are strong enough to win or lose any match at will.
What is the smallest number of rounds after which the friends can get to play a match against each other?

Constraints

2 \leq N \leq 10^{18}

1 \leq A < B \leq N

All input values are integers.

Input

Input is given from Standard Input in the following format:

N A B

Output

Print the smallest number of rounds after which the friends can get to play a match against each other.

Sample Input 1

5 2 4

Sample Output 1

1

If the first friend loses their match and the second friend wins their match, they will both move to table 3 and play each other in the next round.

Sample Input 2

5 2 3

Sample Output 2

2

If both friends win two matches in a row, they will both move to table 1.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;
import java.math.*;
class Main{
	static int mod = 998244353;
public static PrintWriter out = new PrintWriter (new BufferedOutputStream(System.out));
	public static void main(String sp[])throws IOException{
		FastReader sc = new FastReader();
		long n = sc.nextLong();
		long a = sc.nextLong();
		long b = sc.nextLong();
		
		long diff = Math.abs(a-b);
		long min  = Long.MAX_VALUE;
		if(diff%2!=0){
			if(a==1 || b==1 || a==n || b==n){
				System.out.println(1+((diff-1)/2));
			}else{
				min = Math.min(Math.max(a,b)-1 , n - Math.min(a,b));
				long temp1 = (a-1);
				long temp2 = (n-b);
				long temp3 = (b-(a-1));
				long temp4 = (a+(n-b));
				long mod1 = (temp3-1)%2;
				long mod2 = (n-temp4)%2;
				long g = Math.min(temp1 + mod1 + (temp3)/2 , temp2 + mod2 + (temp4)/2);
				System.out.println(Math.min(g,min));
			}	
		}
		else if(diff%2==0){
			System.out.println(diff/2);
		}
	}
	
	
	public static class FastReader {
		BufferedReader br;
		StringTokenizer st;


		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception r) {
					r.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt() {
			return Integer.parseInt(next());//converts string to integer
		}

		double nextDouble() {
			return Double.parseDouble(next());
		}

		long nextLong() {
			return Long.parseLong(next());
		}

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (Exception r) {
				r.printStackTrace();
			}
			return str;
		}
	}

}