You are given n points on Cartesian plane. Every point is a lattice point (i. e. both of its coordinates are integers), and all points are distinct.

You may draw two straight lines (not necessarily distinct). Is it possible to do this in such a way that every point lies on at least one of these lines?

Input

The first line contains one integer n (1 ≤ n ≤ 105) — the number of points you are given.

Then n lines follow, each line containing two integers xi and yi (|xi|, |yi| ≤ 109)— coordinates of i-th point. All n points are distinct.

Output

If it is possible to draw two straight lines in such a way that each of given points belongs to at least one of these lines, print YES. Otherwise, print NO.

Examples

Input

5
0 0
0 1
1 1
1 -1
2 2


Output

YES


Input

5
0 0
1 0
2 1
1 1
2 3


Output

NO

Note

In the first example it is possible to draw two lines, the one containing the points 1, 3 and 5, and another one containing two remaining points.

<image>
#include <bits/stdc++.h>
using std::cin;
using std::cout;
template <class _Tp>
inline _Tp abs(const _Tp &x) {
  return x < 0 ? -x : x;
}
template <class _Tp>
inline _Tp max(const _Tp &a, const _Tp &b) {
  return a > b ? a : b;
}
template <class _Tp>
inline _Tp min(const _Tp &a, const _Tp &b) {
  return a < b ? a : b;
}
template <class _Tp>
inline void inc(_Tp &a, const _Tp &b) {
  if (a < b) a = b;
}
template <class _Tp>
inline void dec(_Tp &a, const _Tp &b) {
  if (a > b) a = b;
}
template <class _Tp>
inline void swp(_Tp &a, _Tp &b) {
  _Tp c = a;
  a = b;
  b = c;
}
template <class _Tp>
inline bool operator==(const _Tp &A, const _Tp &B) {
  return !memcmp(&A, &B, sizeof(_Tp));
}
inline int dcmp(const double &x) { return x > -1e-10 ? x > 1e-10 : -1; }
struct Vector {
  double x, y;
  Vector(const double &A = 0, const double &B = 0) : x(A), y(B) {}
};
inline std::istream &operator>>(std::istream &A, Vector &B) {
  A >> B.x >> B.y;
  return A;
}
inline Vector operator+(const Vector &a, const Vector &b) {
  return Vector(a.x + b.x, a.y + b.y);
}
inline Vector operator-(const Vector &a, const Vector &b) {
  return Vector(a.x - b.x, a.y - b.y);
}
inline Vector operator*(const Vector &a, const double &b) {
  return Vector(a.x * b, a.y * b);
}
inline Vector operator/(const Vector &a, const double &b) {
  return Vector(a.x / b, a.y / b);
}
inline double operator^(const Vector &a, const Vector &b) {
  return a.x * b.y - a.y * b.x;
}
inline double operator*(const Vector &a, const Vector &b) {
  return a.x * b.x + a.y * b.y;
}
inline double dis(const Vector &a, const Vector &b) {
  return sqrt((a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y));
}
struct Circle {
  Vector O;
  double R;
  Circle() {}
  Circle(const Vector &A, const double &B) : O(A), R(B) {}
};
inline std::istream &operator>>(std::istream &A, Circle &B) {
  A >> B.R >> B.O;
  return A;
}
Vector A[100005];
int n;
bool online(const Vector &A, const Vector &B, const Vector &C) {
  return dcmp(((C - A) ^ (B - A)) / dis(A, B)) == 0;
}
bool check(Vector *P, const Vector &A, const Vector &B) {
  std::vector<int> V;
  for (int i = 1; i <= n; ++i)
    if (!online(A, B, P[i])) V.push_back(i);
  for (int i = 2; i < (int)V.size(); ++i)
    if (!online(P[V[0]], P[V[1]], P[V[i]])) return 0;
  return 1;
}
int main() {
  scanf("%d", &n);
  if (n <= 4) return !printf("YES\n");
  for (int i = 1; i <= n; ++i) scanf("%lf%lf", &A[i].x, &A[i].y);
  if (check(A, A[1], A[2]) || check(A, A[1], A[3]) || check(A, A[2], A[3]))
    return !printf("YES\n");
  return !printf("NO\n");
}
