Maximize ab+bc+cd for standard sum of a,b,c,d

'''
If a, b, c, d are positive integers with sum = 63 what is the maximum value
of the expression ab + bc + cd
'''
from timeit import default_timer as timer

def maximize(sum):
    maxExpression = 0
    maxA = 0
    maxB = 0
    maxC = 0
    maxD = 0
    start = timer()
    for a in range(1, sum):
        for b in range(1, sum):
            for c in range(1, sum):
                for d in range(1, sum):
                    if a + b + c + d == sum:
                        expression = a * b + b * c + c * d
                        flag = True
                        if expression > maxExpression:
                            maxExpression = expression
                            maxA = a
                            maxB = b
                            maxC = c
                        maxD = d

    end = timer()
    elapsed = end - start
    print("We know that a,b,c,d > 0 and: a + b + c + d = " + str(sum))
    print("The expression ab + bc + cd gets its maximum value for: ")
    print("a = " + str(maxA) + ", b = " + str(maxB) + ", c = " + str(c) + ", d = " + str(d))
    print("Max expression = " + str(maxExpression))
    print("Execution time = " + str(round(elapsed, 2)) + " seconds.")
    print()


# MAIN FUNCTION
SUM = list(range(5, 70, 5))
for sum in SUM:
    print("************************************************")
    maximize(sum)