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from fractions import gcd

def euler39optimized():
	sum_count = [0] * 1001
	y = 2
	while y**2 <= 500:
		for z in [x for x in range(y) if gcd(y, x) == 1]:
			a = y**2 - z**2
			b = 2*y*z
			c = y**2 + z**2
			for i in range(1, 1001/(a+b+c) + 1):
				sum_count[a*i + b*i + c*i] += 1
		y += 1
	return sum_count.index(max(sum_count))