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
#!/usr/bin/env python

import sys
import math
import itertools as it
from collections import deque

sys.setrecursionlimit(10000000)

n = input()
lst = []
for loop in range(n):
    x, y = map(int, raw_input().split())
    lst.append((x, y))
lst += lst[:2]

ans = 1
for i in range(1, n + 1):
    x0, y0 = lst[i]
    x1, y1 = lst[i - 1]
    x2, y2 = lst[i + 1]
    if (x1 - x0) * (y2 - y0) - (x2 - x0) * (y1 - y0) > 0:
        ans = 0

print ans
