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 <stdio.h>

int main(void) {
  int i, j, n, ans = 1;
  scanf("%d", &n);
  int x[n], y[n];
  scanf("%d%d", &x[0], &y[0]);
  scanf("%d%d", &x[1], &y[1]);
  for(i = 2; i < n; ++i) {
    scanf("%d%d", &x[i], &y[i]);
    if((y[i] - y[i - 2]) * (x[i - 1] - x[i - 2]) - (x[i] - x[i - 2]) * (y[i - 1] - y[i - 2]) < 0) ans = 0;
  }
  if((y[0] - y[n - 2]) * (x[n - 1] - x[n - 2]) - (x[0] - x[n - 2]) * (y[n - 1] - y[n - 2]) < 0) ans = 0;
  if((y[1] - y[n - 1]) * (x[0] - x[n - 1]) - (x[1] - x[n - 1]) * (y[0] - y[n - 1]) < 0) ans = 0;
  printf("%d\n", ans);
  return 0; 
} 
