For a given polygon g, print "1" if g is a convex polygon, "0" otherwise. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.

g is represented by a sequence of points p1, p2,..., pn where line segments connecting pi and pi+1 (1 ≤ i ≤ n-1) are sides of the polygon. The line segment connecting pn and p1 is also a side of the polygon.

Constraints

* 3 ≤ n ≤ 100
* -10000 ≤ xi, yi ≤ 10000
* No point of the polygon will occur more than once.
* Two sides of the polygon can intersect only at a common endpoint.

Input

g is given by coordinates of the points p1,..., pn in the following format:


n
x1 y1
x2 y2
:
xn yn


The first integer n is the number of points. The coordinate of a point pi is given by two integers xi and yi. The coordinates of points are given in the order of counter-clockwise visit of them.

Output

Print "1" or "0" in a line.

Examples

Input

4
0 0
3 1
2 3
0 3


Output

1


Input

5
0 0
2 0
1 1
2 2
0 2


Output

0
#include<bits/stdc++.h>

using namespace std;

typedef complex<double> Point;
const double epx = 1e-10;

bool notNorm(Point a,Point b)
{
    return imag(b*conj(a))<-epx;
}

bool isConvex(vector<Point> points,int sz)
{
    if(sz<3) return false;
    points.push_back(points[0]);
    points.push_back(points[1]);
    for(int i=1;i<=sz;i++)
    {
        if(notNorm(points[i+1]-points[i],points[i-1]-points[i])) return false;
    }
    return true;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);

    int n;
    cin>>n;
    vector<Point> points;
    for(int i=0;i<n;i++)
    {
        int x,y;
        cin>>x>>y;
        points.emplace_back(x,y);
    }
    cout<<isConvex(points,n)<<endl;

    return 0;
}

