Problem:
Score : 700 points

Problem Statement

There are N bags, each containing two white balls. The i-th box contains two balls with integers x_i and y_i written on them, respectively.

For each of these bags, you will paint one of the balls red, and paint the other blue.

Afterwards, the 2N balls will be classified according to color.

Then, we will define the following:

R_{max}: the maximum integer written on a ball painted in red

R_{min}: the minimum integer written on a ball painted in red

B_{max}: the maximum integer written on a ball painted in blue

B_{min}: the minimum integer written on a ball painted in blue

Find the minimum possible value of (R_{max} - R_{min}) \times (B_{max} - B_{min}).

Constraints

1 ≤ N ≤ 200,000

1 ≤ x_i, y_i ≤ 10^9

Input

Input is given from Standard Input in the following format:

N
x_1 y_1
x_2 y_2
:
x_N y_N

Output

Print the minimum possible value.

Sample Input 1

3
1 2
3 4
5 6

Sample Output 1

15

The optimal solution is to paint the balls with x_1, x_2, y_3 red, and paint the balls with y_1, y_2, x_3 blue.

Sample Input 2

3
1010 10
1000 1
20 1020

Sample Output 2

380

Sample Input 3

2
1 1
1000000000 1000000000

Sample Output 3

999999998000000001

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

import java.io.IOException;
import java.io.InputStream;
import java.util.*;
 
public class Main{
	public static void main(String[] args){
		FastScanner sc = new FastScanner();
		long min1 = Long.MAX_VALUE;
		long min2 = Long.MAX_VALUE;
		long max1 = 0;
		long max2 = 0;
		
		int n = sc.nextInt();
		for(int i=0;i<n; i++){
			long x = sc.nextLong();
			long y = sc.nextLong();
			long a1 = Math.min(min1, x);
			long a2 = Math.min(min2, y);
			long a3 = Math.max(max1, x);
			long a4 = Math.max(max2, y);
			long b1 = Math.min(min1, y);
			long b2 = Math.min(min2, x);
			long b3 = Math.max(max1, y);
			long b4 = Math.max(max2, x);
			if((a3-a1)*(a4-a2)<=(b3-b1)*(b4-b2)){
				min1 = a1;
				min2 = a2;
				max1 = a3;
				max2 = a4;
			}else{
				min1 = b1;
				min2 = b2;
				max1 = b3;
				max2 = b4;
			}
		}
		
		System.out.println((max1-min1)*(max2-min2));
		return;
	}
}




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;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; 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() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double nextDouble() { return Double.parseDouble(next());}
}