import sys

#Accomodate for the number of rows to compute
rowstocomp = input('How many rows shall we compute?: ')

#check if input is numeric, if not, end program.
try:
    # if rowstocomp.isnumeric():  -- python3
   rowstocomp = int(rowstocomp)
except ValueError:
   print("Invalid input! ")
   sys.exit()

print('_________________________________________')
print("|x    |y\t|" + u"\u0394" + "y\t|" + u"\u0394" + u"\u00B2" + "y\t|" + u"\u0394" + u"\u00B3" + "y\t|")
print('-----------------------------------------')

#x
if rowstocomp < 7:
    target_range = range (0,7)
else:
    target_range = range(0,rowstocomp)

#y
y = [x**3 - 145 * (x**2) + 5375 * x - 29375 for x in target_range]
if rowstocomp > 7:
    # ycopy = y.copy() -- python3
    ycopy = y[:]

#dy - 1st derivation
deltay = []
for x in range (0,7):
    if x is 6:
        dy = "<>"
    else:
        dy = y[x+1] - y[x]
    deltay.append(dy)

#dy2 - 2nd derivation
deltacubedy = []
for x in range (0,7):
    if x in {5,6}:
        dcy = "<>"
    else:
        dcy = deltay[x+1] - deltay[x]
    deltacubedy.append(dcy)

#dy3 - 3rd derivation
deltasquaredy = []
for x in range (0,7):
    if x in {4,5,6}:
        dsy = "<>"
    else:
        dsy = deltacubedy[x+1] - deltacubedy[x]
    deltasquaredy.append(dsy)

#map
results = dict()
for x in range (0,7):
    results[x] = [str(y[x]),str(deltay[x]),str(deltacubedy[x]),str(deltasquaredy[x])]

#rowstocomp > 7?
grthn7 = False
iter = rowstocomp
if rowstocomp > 7:
    grthn7 = True
    iter = 7

#print results
for key in range (0, iter):
    y = results[key][0]
    deltay = results[key][1]
    deltacubedy = results[key][2]
    deltasquaredy = results[key][3]
    print ("|" + str(key) + "    |" + y + " \t|" + deltay + " \t|" + deltacubedy + " \t|" + deltasquaredy + "\t|")
#handle rows more than 7
else:
    if grthn7:
        y = ycopy
        for x in range (7, rowstocomp):
            if x in {7,8,9}:
                print ("|" + str(x) + "    |" + str(y[x]) + " \t|" + "<>" + " \t|" + "<>" + " \t|" + "<>" + "\t|")
            elif x is 100:
                print ("|" + str(x) + "  |" + str(y[x]) + " \t|" + "<>" + " \t|" + "<>" + " \t|" + "<>" + "\t|")
            else:
                print ("|" + str(x) + "   |" + str(y[x]) + " \t|" + "<>" + " \t|" + "<>" + " \t|" + "<>" + "\t|")

#TODO - As a second test, figure out the first row of a table for the equation: y = x^4 and compute the values of y for x in the range [0,20]
print('_________________________________________')
print('\nSECOND TEST: y = x^4 in range [0,20]')
print('_________________________________________')
print("|x    |y\t|\t\t\t|")
print('-----------------------------------------')

x = list(range(0, 21))
y = list()

for xc in x:
    if xc < 10:
        print("|" + str(xc) + "    |" + str(xc**4) + "\t|")
    else:
        print("|" + str(xc) + "   |" + str(xc**4) + "\t|")