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

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Stanislav Pak
 */
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 {
	class Box {
		final int w;
		final int h;

		Box(int w, int h) {
			this.w = w;
			this.h = h;
		}
	}
    public void solve(int testNumber, InputReader in, OutputWriter out) {
		int n = in.readInt();
		Box[] boxes = new Box[n];
		for (int i = 0; i < n; ++i) {
			int w = in.readInt();
			int h = in.readInt();
			boxes[i] = new Box(w, h);
		}
		int ans = 2000000000;
		for (int height = 1; height <= 1000; ++height) {
			int layCount = 0;
			int width = 0;
			List<Box> bs = new ArrayList<>();
			boolean fail = false;
			for (Box box : boxes) {
				if (box.h > height) {
					if (box.w > height) {
						fail = true;
						break;
					}
					width += box.h;
					++layCount;
				} else {
					bs.add(box);
				}
			}
			if (fail || layCount > n / 2) {
				continue;
			}
			int k = n / 2 - layCount;
			Collections.sort(bs, new Comparator<Box>() {
				public int compare(Box o1, Box o2) {
					return (o1.h - o1.w) - (o2.h - o2.w);
				}
			});
			for (int i = 0; i < bs.size(); ++i) {
				Box b = bs.get(i);
				if (k > 0) {
					if (b.w > b.h && b.w <= height) {
						width += b.h;
						--k;
					} else {
						width += b.w;
					}
				} else {
					width += b.w;
				}
			}
			ans = Math.min(ans, height * width);
		}
		out.printLine(ans);
    }
}

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 close() {
		writer.close();
	}

	public void printLine(int i) {
		writer.println(i);
	}
}

