Problem:
Convex Hull

Find the convex hull of a given set of points P. In other words, find the smallest convex polygon containing all the points of P. Here, in a convex polygon, all interior angles are less than or equal to 180 degrees.

Please note that you should find all the points of P on both corner and boundary of the convex polygon.

Input

n
x1 y1
x2 y2
:
xn yn

The first integer n is the number of points in P. The coordinate of the i-th point pi is given by two integers xi and yi.

Output

In the first line, print the number of points on the corner/boundary of the convex polygon. In the following lines, print x y coordinates of the set of points.
The coordinates should be given in the order of counter-clockwise visit of them starting from the point in P with the minimum y-coordinate, or the leftmost such point in case of a tie.

Constraints

3 ≤ n ≤ 100000

-10000 ≤ xi, yi ≤ 10000

No point in the P will occur more than once.

Sample Input 1

7
2 1
0 0
1 2
2 2
4 2
1 3
3 3

Sample Output 1

5
0 0
2 1
4 2
3 3
1 3

Sample Input 2

4
0 0
2 2
0 2
0 1

Sample Output 2

4
0 0
2 2
0 2
0 1

Solution in Python3 (judge verdict: Wrong Answer)

#!/usr/bin/env python
# -*- coding: utf-8 -*-

"""
input:
7
2 1
0 0
1 2
2 2
4 2
1 3
3 3

output:
5
0 0
2 1
4 2
3 3
1 3

The operator module functions allow multiple levels of sorting. For example, to sort by grade then by age:

sorted(student_tuples, key=itemgetter(1,2))
[('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)]

sorted(student_objects, key=attrgetter('grade', 'age'))
[('john', 'A', 15), ('dave', 'B', 10), ('jane', 'B', 12)]
"""

import sys
from operator import attrgetter

EPS = 1e-9


def cross(a, b):
    return a.real * b.imag - a.imag * b.real


def dot(a, b):
    return a.real * b.real + a.imag * b.imag


def check_ccw(p0, p1, p2):
    a, b = p1 - p0, p2 - p0
    if cross(a, b) > EPS:
        # print('COUNTER_CLOCKWISE')
        flag = 1
    elif cross(a, b) < -1 * EPS:
        # print('CLOCKWISE')
        flag = -1
    elif dot(a, b) < -1 * EPS:
        # print('ONLINE_BACK')
        flag = 2
    elif abs(a) < abs(b):
        # print('ONLINE_FRONT')
        flag = -2
    else:
        # print('ON_SEGMENT')
        flag = 0
    return flag


def convex_check_Andrew(_polygon):
    upper, lower = list(), list()
    _polygon.sort(key=attrgetter('real', 'imag'))

    upper.extend((_polygon[0], _polygon[1]))
    lower.extend((_polygon[-1], _polygon[-2]))

    for i in range(2, points):
        n1 = len(upper)
        if n1 >= 2 and check_ccw(upper[n1 - 2], upper[n1 - 1], _polygon[i]) != -1:
            n1 -= 1
            upper.pop()
        upper.append(_polygon[i])

    for j in range(points - 3, -1, -1):
        n2 = len(lower)
        if n2 >= 2 and check_ccw(lower[n2 - 2], lower[n2 - 1], _polygon[j]) != -1:
            n2 -= 1
            lower.pop()
        lower.append(_polygon[j])

    lower.reverse()
    for k in range(len(upper) - 2, 0, -1):
        lower.append(upper[k])

    return lower


if __name__ == '__main__':
    _input = sys.stdin.readlines()
    points = int(_input[0])
    p_info = map(lambda x: x.split(), _input[1:])

    polygon = [int(x) + int(y) * 1j for x, y in p_info]
    ans = convex_check_Andrew(polygon)
    print(len(ans))
    for ele in ans:
        print(int(ele.real), int(ele.imag))