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

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

class TaskB {
    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int N = in.nextInt();
        int[] W = new int[N];
        int[] H = new int[N];
        for (int i = 0; i < N; i++) {
            W[i] = in.nextInt();
            H[i] = in.nextInt();
        }

        int can = N / 2;
        int[] A = new int[N];
        int ans = Integer.MAX_VALUE;
        int[] hs = new int[2];
        for (int ph = 0; ph < N; ph++) {
            hs[0] = H[ph];
            hs[1] = W[ph];
            for (int hh = 0; hh < 2; hh++) {
                int h = hs[hh];
                int K = 0;
                boolean ok = true;
                int total = 0;
                int crtCan = can - hh;
                total += hh == 0 ? W[ph] : H[ph];
                for (int i = 0; i < N; i++) {
                    if (i == ph) continue;

                    if (W[i] <= h && H[i] <= h) {
                        if (H[i] < W[i]) {
                            A[K++] = H[i] - W[i];
                        }
                        else {
                            A[K++] = 0;
                        }
                        total += W[i];
                    }
                    else if (H[i] <= h) {
                        total += W[i];
                    }
                    else if (W[i] <= h) {
                        total += H[i];
                        crtCan--;
                    }
                    else {
                        ok = false;
                        break;
                    }

                }
                if (!ok || crtCan < 0) {
                    continue;
                }
                Arrays.sort(A, 0, K);
                int diff = 0;
                for (int i = 0; i < K && i < crtCan; i++) {
                    diff += A[i];
                }
                int crt = total + diff;
                ans = Math.min(ans, crt * h);
            }
        }

        out.println(ans);
    }
}

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

    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 nextInt() {
        return Integer.parseInt(nextString());
    }

    public String nextString() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuffer res = new StringBuffer();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));

        return res.toString();
    }

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

}

