Recently Vasya learned that, given two points with different x coordinates, you can draw through them exactly one parabola with equation of type y = x^2 + bx + c, where b and c are reals. Let's call such a parabola an U-shaped one.

Vasya drew several distinct points with integer coordinates on a plane and then drew an U-shaped parabola through each pair of the points that have different x coordinates. The picture became somewhat messy, but Vasya still wants to count how many of the parabolas drawn don't have any drawn point inside their internal area. Help Vasya.

The internal area of an U-shaped parabola is the part of the plane that lies strictly above the parabola when the y axis is directed upwards.

Input

The first line contains a single integer n (1 ≤ n ≤ 100 000) — the number of points.

The next n lines describe the points, the i-th of them contains two integers x_i and y_i — the coordinates of the i-th point. It is guaranteed that all points are distinct and that the coordinates do not exceed 10^6 by absolute value.

Output

In the only line print a single integer — the number of U-shaped parabolas that pass through at least two of the given points and do not contain any of the given points inside their internal area (excluding the parabola itself).

Examples

Input


3
-1 0
0 2
1 0


Output


2


Input


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


Output


1

Note

On the pictures below all U-shaped parabolas that pass through at least two given points are drawn for each of the examples. The U-shaped parabolas that do not have any given point inside their internal area are drawn in red. 

<image> The first example.  <image> The second example. 
import java.io.*;
import java.util.*;

public class F549 {
	public static void main(String[] args) { new F549(); }
	FS in = new FS();
	PrintWriter out = new PrintWriter(System.out);

	int n;
	long MAX = 1000000, oo = MAX * (MAX + 1) + 1;
	vec[] x;

	F549() {
		n = in.nextInt();
		x = new vec[n];
		for (int i = 0; i < n; i++) {
			long nx = in.nextLong();
			long ny = in.nextLong() - nx * nx;
			x[i] = new vec(nx, ny);
		}
		HashMap<Long, Long> top = new HashMap<>();
		for (vec v : x) {
			top.putIfAbsent(v.x, -oo); 
			top.put(v.x, max(v.y, top.get(v.x)));
		}
		
		int ptr = 0;
		x = new vec[top.size()];
		for (long key : top.keySet()) 
			x[ptr++] = new vec(key, top.get(key));
		
		convexHull CH = new convexHull();
		CH.getHull(x);

		int k = CH.upper.length;
		out.println(k - 1);
		out.close();
	}

	class convexHull{
		vec[] upper, lower;

		vec[] removeDupes(vec[] pts) {
			HashSet<vec> set = new HashSet<>();
			for (vec v : pts) set.add(v);
			int ptr = 0; pts = new vec[set.size()];
			for (vec v : set) pts[ptr++] = v;
			return pts;
		}

		vec[] getHull(vec[] pts) {
			pts = pts.clone();
			Arrays.sort(pts);
			if (pts.length < 3) return upper = lower = pts;
			int n = pts.length, j = 2, k = 2;
			vec[] lo = new vec[n];
			lo[0] = pts[0];
			lo[1] = pts[1];
			for (int i = 2; i < n; i++) {
				vec p = pts[i];
				while (j > 1 && !right(lo[j - 2], lo[j - 1], p)) j--;
				lo[j++] = p;
			}
			vec[] hi = new vec[n];
			hi[0] = pts[n - 1];
			hi[1] = pts[n - 2];
			for (int i = n - 3; i >= 0; i--){
				vec p = pts[i];
				while (k > 1 && !right(hi[k - 2], hi[k - 1], p)) k--;
				hi[k++] = p;
			}
			vec[] hull = new vec[j + k - 2];
			for (int i = 0; i < k; i++) hull[i] = hi[i];
			for (int i = 1; i < j - 1; i++) hull[k + i - 1] = lo[i];
			upper = new vec[k];
			for (int i = 0; i < k; i++) upper[i] = hi[k - i - 1];
			return hull;
		}

		boolean right(vec a, vec b, vec c) {
			return (b.sub(a)).cross(c.sub(a)) > 0;
		}
	}

	class vec implements Comparable<vec> {
		long x, y;
		vec (long xx, long yy) { x = xx; y = yy; }
		vec sub(vec o) { return new vec(x - o.x, y - o.y); }

		long cross(vec o) { return x * o.y - y * o.x; }

		public int compareTo(vec o) {
			if (x != o.x) return Long.compare(x, o.x);
			return Long.compare(y, o.y);
		}
	}
	
	int abs(int x) { if (x < 0) return -x; return x; }
	long abs(long x) { if (x < 0) return -x; return x; }
	int min(int a, int b) { if (a < b) return a; return b; }	
	int max(int a, int b) { if (a > b) return a; return b; }	
	long min(long a, long b) { if (a < b) return a; return b; }	
	long max(long a, long b) { if (a > b) return a; return b; }	
	int gcd(int a, int b) { while (b > 0) { a = b^(a^(b = a)); b %= a; } return a; }
	long gcd(long a, long b) { while (b > 0) { a = b^(a^(b = a)); b %= a; } return a; }
	long lcm(int a, int b) { return (((long) a) * b) / gcd(a, b); }
	long lcm(long a, long b) { return (a * b) / gcd(a, b); }

	void sort(int[] arr) {
		int sz = arr.length, j;
		Random r = new Random();
		for (int i = 0; i < sz; i++) {
			j = r.nextInt(i + 1);
			arr[i] = arr[j]^(arr[i]^(arr[j] = arr[i]));
		} Arrays.sort(arr);
	}

	class FS {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		String next() {
			while (!st.hasMoreTokens()) {
				try { st = new StringTokenizer(br.readLine()); }
				catch (Exception e) {}
			} return st.nextToken();
		}
		int nextInt() { return Integer.parseInt(next()); }
		long nextLong() { return Long.parseLong(next()); }
		double nextDouble() { return Double.parseDouble(next()); }
	}
}

