A Pythagorean triple is a set of three integer numbers that form a right triangle. The sum of the squares of the two smaller numbers should equal the square of the largest number. Given three numbers a, b and c (c being the largest):

a^2 + b^2 = c^2

Furthermore, a Pythagorean triple is said to be primitive if the three numbers are pairwise coprime - that is, the greatest common prime factor between any two numbers is 1.

Create a function that takes an array of three numbers (unordered) and returns true if the numbers constitute a primitive Pythagorean triple, false otherwise.

Examples

is_prim_pyth_triple([4, 5, 3]) ➞ true

is_prim_pyth_triple([7, 12, 13]) ➞ false

is_prim_pyth_triple([39, 15, 36]) ➞ false
# Pythagorean triple, but not primitive.

is_prim_pyth_triple([77, 36, 85]) ➞ true

Notes

N/A