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.io.*;
import java.util.*;

public class Main {
	static Scanner sc = new Scanner(System.in);
	static PrintWriter out = new PrintWriter(System.out);

	static boolean lie(ArrayList<point> q) {
		int m = q.size();
		if (m <= 2) return true;
		
		line l = new line(q.get(0), q.get(1));
		for (int i = 0; i < m; i++) {
			if (!l.lie(q.get(i)))  return false;
		}
		
		return true;
	}

	public static void main(String[] args) throws Exception {
		int n = sc.nextInt();
		point p[] = new point[n];

		if (n < 5) {
			System.out.println("YES");
			return;
		}

		for (int i = 0; i < n; i++) {
			p[i] = new point(sc.nextInt(), sc.nextInt());
		}

		line l1 = new line(p[0], p[1]);
		line l2 = new line(p[1], p[2]);
		line l3 = new line(p[2], p[0]);

		ArrayList<point> u = new ArrayList<>();
		ArrayList<point> v = new ArrayList<>();
		ArrayList<point> w = new ArrayList<>();

		for (int i = 0; i < n; i++) {
			point cur = p[i];
			if (!l1.lie(cur)) {
				u.add(cur);
			}
			if (!l2.lie(cur)) {
				v.add(cur);
			}
			if (!l3.lie(cur)) {
				w.add(cur);
			}
		}

		out.println(lie(u) || lie(v) || lie(w) ? "YES" : "NO");
		out.close();
	}

}

class point {
	long x, y;

	point(long x, long y) {
		this.x = x;
		this.y = y;
	}
}

class line {
	long a, b, c;

	line(point first, point second) {
		a = first.y - second.y;
		b = -first.x + second.x;
		c = first.x * a + first.y * b;
	}

	boolean lie(point first) {
		return a * first.x + b * first.y == c;
	}
}

class Scanner {
	StringTokenizer st;
	BufferedReader br;

	public Scanner(InputStream system) {
		br = new BufferedReader(new InputStreamReader(system));
	}

	public Scanner(String file) throws Exception {
		br = new BufferedReader(new FileReader(file));
	}

	public String next() throws IOException {
		while (st == null || !st.hasMoreTokens())
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	public String nextLine() throws IOException {
		return br.readLine();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	public Long nextLong() throws IOException {
		return Long.parseLong(next());
	}
}