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: Accepted)

// package atcoder.arc.arc073;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class Main {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();
        long[][] balls = in.nextLongTable(n, 2);
        for (int i = 0; i < n ; i++) {
            if (balls[i][0] > balls[i][1]) {
                long tmp = balls[i][0];
                balls[i][0] = balls[i][1];
                balls[i][1] = tmp;
            }
        }
        Arrays.sort(balls, (a, b) -> Long.compare(a[0], b[0]));

        if (n == 1) {
            out.println(0);
            out.flush();
            return;
        }

        long ptnA = solveA(balls);
        long ptnB = solveB(balls);

        out.println(Math.min(ptnA, ptnB));
        out.flush();
    }

    private static long solveB(long[][] balls) {
        int n = balls.length;
        long[] yminUp = new long[n+1];
        long[] ymaxUp = new long[n+1];
        long[] yminDw = new long[n+1];
        long[] ymaxDw = new long[n+1];

        yminUp[0] = yminDw[0] = Long.MAX_VALUE;
        for (int i = 0; i < n ; i++) {
            yminUp[i+1] = Math.min(yminUp[i], balls[i][1]);
            ymaxUp[i+1] = Math.max(ymaxUp[i], balls[i][1]);
            yminDw[i+1] = Math.min(yminDw[i], balls[n-1-i][1]);
            ymaxDw[i+1] = Math.max(ymaxDw[i], balls[n-1-i][1]);
        }

        long best = Long.MAX_VALUE;
        for (int take = 1 ; take < n ; take++) {
            long bmin = Math.min(yminUp[take], balls[take][0]);
            long bmax = Math.max(ymaxUp[take], balls[n-1][0]);
            long rmin = Math.min(yminDw[n-take], balls[0][0]);
            long rmax = Math.max(ymaxDw[n-take], balls[take-1][0]);
            best = Math.min(best, (rmax-rmin)*(bmax-bmin));
        }
        return best;
    }

    private static long solveA(long[][] balls) {
        int n = balls.length;
        long rmin = Long.MAX_VALUE;
        long rmax = Long.MIN_VALUE;
        long bmin = Long.MAX_VALUE;
        long bmax = Long.MIN_VALUE;
        for (int i = 0; i < n ; i++) {
            rmin = Math.min(rmin, balls[i][0]);
            rmax = Math.max(rmax, balls[i][0]);
            bmin = Math.min(bmin, balls[i][1]);
            bmax = Math.max(bmax, balls[i][1]);
        }
        return (rmax-rmin)*(bmax-bmin);
    }


    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int[] nextInts(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }

        private int[][] nextIntTable(int n, int m) {
            int[][] ret = new int[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextInt();
                }
            }
            return ret;
        }

        private long[] nextLongs(int n) {
            long[] ret = new long[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextLong();
            }
            return ret;
        }

        private long[][] nextLongTable(int n, int m) {
            long[][] ret = new long[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    ret[i][j] = nextLong();
                }
            }
            return ret;
        }

        private double[] nextDoubles(int n) {
            double[] ret = new double[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextDouble();
            }
            return ret;
        }

        private int next() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public char nextChar() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            if ('a' <= c && c <= 'z') {
                return (char) c;
            }
            if ('A' <= c && c <= 'Z') {
                return (char) c;
            }
            throw new InputMismatchException();
        }

        public String nextToken() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public long nextLong() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c-'0';
                c = next();
            } while (!isSpaceChar(c));
            return res*sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }

    static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }
}