# Author     : Manfred Scheucher
# Date       : Jul 25 2015
# Description: This python script generates an LP which can be solved by an
#              LP-solver. The following command gives an example how to
#              use this script with GLPK:
#                     python b.py 5 > 5.lp && glpsol --lp 5.lp

from sys import argv
from itertools import combinations

assert(1^1==0) # use python, not sage

def b(x):
	return (n*'0'+bin(x)[2:])[-n:] # binary rep. with leading zeroes

def v(x,y):
	return " v_"+str(x+1)+"_"+str(y+1)

n = int(argv[1])

i = 0

print "Maximize"
print " obj: "+'+'.join(v(x,y) for x in range(n) for y in range(n))


print "Subject To"
for x in range(n):
	for y in range(n):
		print " c"+str(i)+":"+'+'.join(('3' if e==0 and d==0 else '1')+v(x+d,y+e) for d in [-1,0,1] for e in [-1,0,1])+"<= 4"
		i+=1

for x in range(-1,n+1):
	for y in range(-1,n+1):
		if x not in range(n) or y not in range(n):
			print " c"+str(i)+":"+v(x,y)+"= 0"
			i+=1

print "Binary"
for x in range(-1,n+1):
	for y in range(-1,n+1):
		print v(x,y)

print "End"