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;
 
using ll = long long; using ld = long double; using ull = unsigned long long; using uint = unsigned int;
using vi  = vector<int>; using vb  = vector<bool>; using vd  = vector<double>; using vl  = vector<ll>;
using vvi = vector<vi>;  using vvb = vector<vb>;   using vvd = vector<vd>;     using vvl = vector<vl>;
 
#define REP(i,n) for(ll i=0; i<(n); ++i)
#define FOR(i,b,n) for(ll i=(b); i<(n); ++i)
#define ALL(v) (v).begin(), (v).end()
#define TEN(x) ((ll)1e##x)
 
template<typename T> inline string join(const vector<T>& vec, string sep = " ") { stringstream ss; REP(i, vec.size()) ss << vec[i] << ( i+1 == vec.size() ? "" : sep ); return ss.str(); }
 
 
///////////////
 
#define EPS (1e-10)
#define NEXT(x, i) (x[(i + 1) % x.size()])
 
template<class T> using CR = const T &;
using P = complex<ld>;
using G = vector<P>;
 
int sgn(ld a, ld b = 0) {
    if (a > b + EPS) return 1;
    if (a < b - EPS) return -1;
    return 0;
}
 
ld dot(P a, P b) { return real(conj(a)*b); }
ld cross(P a, P b) { return imag(conj(a)*b); }
 
int ccw(P a, P b, P c) {
    b -= a;
    c -= a;
    if (sgn(cross(b, c))) return sgn(cross(b, c)); // clockwise or counter clockwise
    if (sgn(dot(b, c)) == -1) return 2;            // c--a--b
    if (sgn(norm(b), norm(c)) == -1) return -2;    // a--b--c
    return 0;                                      // a--c--b
}

bool is_convex(CR<G> g, bool strict = false) {
	REP(i, g.size()) {
		int c = ccw(g[(i + g.size() - 1) % g.size()], g[i], g[(i + 1) % g.size()]);
		if (c == -1 || (strict && c != 1)) return false;
	}
	return true;
}
 
 
//////////////
 
int main() {
#ifdef INPUT_FROM_FILE
    ifstream cin("sample.in");
    ofstream cout("sample.out");
#endif
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(30);
    ll n; cin >> n;
 
    G g(n);
    REP(i,n){
        ld x, y;
        cin >> x >> y;
        g[i] = { x, y };
    }
    cout << is_convex(g) << endl;
 
    return 0;
}