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>
import math
import sys

from collections import defaultdict

def solve(io):
  N = io.readInt()
  
  P = [None] * N
  for i in range(0, N):
    X = io.readInt()
    Y = io.readInt()
    P[i] = (X, Y)
  
  if N <= 4:
    io.println("YES")
    return
  
  for i in range(0, 3):
    P[0], P[i] = P[i], P[0]
    if can(P):
      io.println("YES")
      return
  
  io.println("NO")

def can(P):
  slopes = makeSlopeDict(P)
  
  if len(slopes) <= 2:
    return True
  
  matches = 0
  others = []
  for _, v in slopes.items():
    if len(v) > 1:
      matches += 1
    else:
      others += v
  
  if matches > 1:
    return False
  
  line = makeSlopeDict(others)
  return len(line) <= 1

def makeSlopeDict(pts):
  slopes = defaultdict(set)
  for i in range(1, len(pts)):
    dx = pts[i][0] - pts[0][0]
    dy = pts[i][1] - pts[0][1]
    if dy < 0:
      dx *= -1
      dy *= -1
    if dx != 0 and dy != 0:
      g = math.gcd(dx, dy)
      v = (dx / g, dy / g)
    elif dx == 0 and dy != 0:
      v = (0, 1)
    elif dx != 0 and dy == 0:
      v = (1, 0)
    else:
      v = (0, 0)
    slopes[v].add(pts[i])
  return slopes

# +---------------------+
# | TEMPLATE CODE BELOW |
# |    DO NOT MODIFY    |
# +---------------------+

# TODO: maybe reading byte-by-byte is faster than reading and parsing tokens.
class IO:
  input = None
  output = None
  raw = ""
  buf = []
  pos = 0
  
  def __init__(self, inputStream, outputStream):
    self.input = inputStream
    self.output = outputStream
  
  def readToBuffer(self):
    self.raw = self.input.readline().rstrip('\n')
    self.buf = self.raw.split()
    self.pos = 0
  
  def readString(self):
    while self.pos == len(self.buf):
      self.readToBuffer()
    ans = self.buf[self.pos]
    self.pos += 1
    return ans
  
  def readInt(self):
    return int(self.readString())
  
  def readFloat(self):
    return float(self.readString())
  
  def readStringArray(self, N, offset = 0):
    arr = [ None ] * offset
    for _ in range(0, N):
      arr.append(self.readString())
    return arr
  
  def readIntArray(self, N, offset = 0):
    arr = [ None ] * offset
    for _ in range(0, N):
      arr.append(self.readInt())
    return arr
  
  def readFloatArray(self, N, offset = 0):
    arr = [ None ] * offset
    for _ in range(0, N):
      arr.append(self.readFloat())
    return arr
  
  def readLine(self):
    while self.pos == len(self.buf):
      self.readToBuffer()
    if self.pos > 0:
      raise ValueError("Cannot call readline in the middle of a line.")
    return self.raw
  
  def print(self, s):
    self.output.write(str(s))
  
  def println(self, s):
    self.print(s)
    self.print('\n')
  
  def flushOutput(self):
    self.output.flush()

pythonIO = IO(sys.stdin, sys.stdout)
solve(pythonIO)
pythonIO.flushOutput()
