The Pythagorean formula is a²+b²=c² where a and b are the lengths of the "legs" (shorter sides) of a right triangle and c is the length of the hypotenuse (longest side) of the same right triangle. The numbers a, b and c are called a Pythagorean triple.

There are combinations of integers which are Pythagorean triples like 3, 4 and 5: 3²+4²=5². You goal is write a program to print integer Pythagorean triples.

Your program should first prompt for and read a number n which will be maximum value for c. Then it should test each value of c in a loop to see if there are any integers a and b which work with c to form a Pythagorean triple. If so, then the values for a, b and c should be printed.

Suppose the number entered for maximum c is 20. The program will output

3 4 5
6 8 10
5 12 13
9 12 15
8 15 17
12 16 20

It should be clear that there will be an outer loop incrementing c from 1 to n. Then inside this loop the program needs to try all values of a from 1 to c-1. For each value of a there is only 1 reasonable value of b to try: sqrt(c*c-a*a). This value for b needs to be tested to see if a*a+b*b == c*c. If the test passes the triple should be printed and it is time to break out of the inner loop.

After reading n use an assert statement to verify that n is greater than 0 and less than or equal to 1000.