Many years have passed, and n friends met at a party again. Technologies have leaped forward since the last meeting, cameras with timer appeared and now it is not obligatory for one of the friends to stand with a camera, and, thus, being absent on the photo.

Simply speaking, the process of photographing can be described as follows. Each friend occupies a rectangle of pixels on the photo: the i-th of them in a standing state occupies a wi pixels wide and a hi pixels high rectangle. But also, each person can lie down for the photo, and then he will occupy a hi pixels wide and a wi pixels high rectangle.

The total photo will have size W × H, where W is the total width of all the people rectangles, and H is the maximum of the heights. The friends want to determine what minimum area the group photo can they obtain if no more than n / 2 of them can lie on the ground (it would be strange if more than n / 2 gentlemen lie on the ground together, isn't it?..)

Help them to achieve this goal.

Input

The first line contains integer n (1 ≤ n ≤ 1000) — the number of friends.

The next n lines have two integers wi, hi (1 ≤ wi, hi ≤ 1000) each, representing the size of the rectangle, corresponding to the i-th friend.

Output

Print a single integer equal to the minimum possible area of the photo containing all friends if no more than n / 2 of them can lie on the ground.

Examples

Input

3
10 1
20 2
30 3


Output

180


Input

3
3 1
2 2
4 3


Output

21


Input

1
5 10


Output

50
import java.util.List;
import java.io.IOException;
import java.io.OutputStreamWriter;
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.math.BigInteger;
import java.util.Collections;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        OutputWriter out = new OutputWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskB {

    int n;
    int INF = (int) 1e7;

    class Person {
        int w;
        int h;

        public Person(int w, int h) {
            this.w = w;
            this.h = h;
        }
    }

    public void solve(int testNumber, InputReader in, OutputWriter out) {
        n = in.readInt();
        Person[] p = new Person[n];
        for (int i = 0; i < n; i++) {
            p[i] = new Person(in.readInt(), in.readInt());
        }

        long best = Integer.MAX_VALUE;

        for (int maxH = 1; maxH <= 1000; maxH++) {
            int cnt = 0;
            int wdth = 0;
            ArrayList<Integer> remaining = new ArrayList<Integer>();

            for (int i = 0; i < n; i++) {

                if (p[i].h > p[i].w) {
                    if (p[i].h <= maxH) {
                        wdth += p[i].w;
                    }
                    else if (p[i].w <= maxH) {
                        wdth += p[i].h;
                        cnt++;
                    }
                    else {
                        wdth = INF;
                        break;
                    }
                }

                else {
                    if (p[i].h > maxH) {
                        wdth = INF;
                        break;
                    }
                    else if (p[i].w <= maxH) {
                        remaining.add(p[i].h - p[i].w);
                    }
                    wdth += p[i].w;
                }
            }

            if (wdth >= INF || cnt * 2 > n) continue;

            Collections.sort(remaining);
            for (int i = 0; i < remaining.size() && 2 * (cnt + 1) <= n; i++) {
                wdth += remaining.get(i);
                cnt++;
            }

            best = Math.min(best, wdth * maxH);
        }

        out.printLine(best);
    }
}

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

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

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

    public boolean isSpaceChar(int c) {
        if (filter != null)
            return filter.isSpaceChar(c);
        return isWhitespace(c);
    }

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

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

class OutputWriter {
    private final PrintWriter writer;

    public OutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
    }

    public void print(Object...objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void printLine(Object...objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

}

