You are given n points on Cartesian plane. Every point is a lattice point (i. e. both of its coordinates are integers), and all points are distinct.

You may draw two straight lines (not necessarily distinct). Is it possible to do this in such a way that every point lies on at least one of these lines?

Input

The first line contains one integer n (1 ≤ n ≤ 105) — the number of points you are given.

Then n lines follow, each line containing two integers xi and yi (|xi|, |yi| ≤ 109)— coordinates of i-th point. All n points are distinct.

Output

If it is possible to draw two straight lines in such a way that each of given points belongs to at least one of these lines, print YES. Otherwise, print NO.

Examples

Input

5
0 0
0 1
1 1
1 -1
2 2


Output

YES


Input

5
0 0
1 0
2 1
1 1
2 3


Output

NO

Note

In the first example it is possible to draw two lines, the one containing the points 1, 3 and 5, and another one containing two remaining points.

<image>
import java.util.*;

public class PairOfLines {

    static boolean checkIfOnLine (long mNum, long mDen, int x1, int y1, int x2, int y2) {
        if (mDen == 0) {
            return x1 == x2;
        }
        long a = mDen * (y2 - y1);
        long b = mNum * (x2 - x1);
        return a == b;
    }

    static List<Integer> indiciesNotOnLine (int[][] points, long mNum, long mDen, int x, int y) {
        List<Integer> result = new ArrayList<>();
        for (int i = 0; i < points.length; i++) {
            if (!checkIfOnLine(mNum, mDen, x, y, points[i][0], points[i][1])) {
                result.add(i);
            }
        }
        return result;
    }

    static boolean isTwoOnLine (int[][] points, int i, int j) {
        int x1 = points[i][0];
        int y1 = points[i][1];
        int x2 = points[j][0];
        int y2 = points[j][1];
        List<Integer> otherIndicies = indiciesNotOnLine(points, y2 - y1, x2 - x1, x1, y1);

        if (otherIndicies.size() <= 2) {
            return true;
        }

        // make a line with first 2 points
        int otherX1 = points[otherIndicies.get(0)][0];
        int otherY1 = points[otherIndicies.get(0)][1];
        int otherX2 = points[otherIndicies.get(1)][0];
        int otherY2 = points[otherIndicies.get(1)][1];
        // make sure all points in otherIndicies are on this line
        for (int k = 0; k < otherIndicies.size(); k++) {
            int index = otherIndicies.get(k);
            boolean isPtOnLine = checkIfOnLine(otherY2 - otherY1, otherX2 - otherX1, otherX1, otherY1, points[index][0], points[index][1]);
            if (!isPtOnLine) {
                return false;
            }
        }
        return true;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int[][] points = new int[n][2];
        for (int i = 0; i < n; i++) {
            points[i][0] = sc.nextInt();
            points[i][1] = sc.nextInt();
        }

        // pick 3 points
        if (n <= 2) {
            System.out.println("YES");
            System.exit(0);
        }

        boolean is12 = isTwoOnLine(points, 0, 1);
        boolean is13 = isTwoOnLine(points, 0, 2);
        boolean is23 = isTwoOnLine(points, 1, 2);
        if (is12 || is13 || is23) {
            System.out.println("YES");
        } else {
            System.out.println("NO");
        }
    }
}
