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  x 1  y 1  x 2  y 2 : x n  y n  The first integer n is the number of points in P . The coordinate of the i -th point p i is given by two integers x i and y i . 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 ≤ x i , y i ≤ 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 (Python):
def isCLKWISE(ph):
    return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph):
    return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P.sort()
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph):
    return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P.sort()
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph):
    return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P.sort()
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph):
    return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P.sort()
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph):
    return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n:
    P.append([int(x) for x in input().split()])
      
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = []
for i in n : P.append([int(x) for x in input().split()])
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:] :
        phU.append(p)
        while(True) :
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1] :
        phL.append(p)
        while(True) :
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P) :
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:] :
        phU.append(p)
        while(True) :
            if isCLKWISE(phU) : break
            else :
                del phU[-2]
                if len(phU) == 2 : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1] :
        phL.append(p)
        while(True) :
            if isCLKWISE(phL) : break
            else :
                del phL[-2]
                if len(phL) == 2 : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            if len(phU) == 2 : break
            else :
                if isCLKWISE(phU) : break

    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            if len(phL) == 2 : break
            else :
                if isCLKWISE(phL) : break

                
                
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            if len(phU) == 2 : break
            else :
                if isCLKWISE(phU) : break

    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            if len(phL) == 2 : break
            else :
                if isCLKWISE(phL) : break

                
                
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            if len(phU) == 2 : break
            else :
                if isCLKWISE(phU) : break

    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            if len(phL) == 2 : break
            else :
                if isCLKWISE(phL) : break

                
                
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            if len(phU) == 2 : break
            else :
                if isCLKWISE(phU) : break

    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            if len(phL) == 2 : break
            else :
                if isCLKWISE(phL) : break

                
                
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError:
                break

    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError:
                break
                
                
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError:
                break

    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError:
                break
                
                
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            try :
                if isCLKWISE(phU) : break
                else : del phU[-2]
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            try :
                if isCLKWISE(phL) : break
                else : del phL[-2]
            except IndexError : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            try :
                if isCLKWISE(phU) : break
                else : del phU[-2]
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            try :
                if isCLKWISE(phL) : break
                else : del phL[-2]
            except IndexError : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            try :
                if isCLKWISE(phU) : break
                else : del phU[-2]
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            try :
                if isCLKWISE(phL) : break
                else : del phL[-2]
            except IndexError : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        while(True):
            try :
                if isCLKWISE(phU) : break
                else : del phU[-2]
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        while(True):
            try :
                if isCLKWISE(phL) : break
                else : del phL[-2]
            except IndexError : break
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:] :
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1] :
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break
      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break
      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(y) for y in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break
      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(y) for y in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break
      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(y) for y in input().split()] for _ in n]
Q = ConvexHullScan(P)
Q.reverse()
print(len(Q))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(Q)])[2]
R = Q[idx:] + Q[:idx]
for r in R : print(r[0],r[1])

Solution (Python):
def isCLKWISE(ph) : return not ((ph[-1][0] - ph[-3][0])*(- ph[-3][1] + ph[-2][1]) - (ph[-2][0] - ph[-3][0])*(- ph[-3][1] + ph[-1][1] ) < 0)
      
def ConvexHullScan(P):
    P = sorted(P)
    phU = [P[0],P[1]]
    for p in P[2:]:
        phU.append(p)
        if isCLKWISE(phU) : continue
        while(True):
            del phU[-2]
            try:
                if isCLKWISE(phU) : break
            except IndexError : break
    phL = [P[-1],P[-2]]
    for p in P[-3::-1]:
        phL.append(p)
        if isCLKWISE(phL) : continue
        while(True):
            del phL[-2]
            try:
                if isCLKWISE(phL) : break
            except IndexError : break
      
    ph = phU + phL[1:-1]
    return ph
  
n = range(int(input()))
P = [[int(x) for x in input().split()] for _ in n]
P = ConvexHullScan(P)
P.reverse()
print(len(P))
idx = min([[x[1][1],x[1][0],x[0]] for x in enumerate(P)])[2]
P = P[idx:] + P[:idx]
for p in P : print(p[0],p[1])