four different integers exist, what is the least product value?

Question

Four different positive integers $a, b, c, d$ are such that $a^2 + b^2 = c^2 + d^2$. What is the smallest possible value of $abcd$?

$$a^2 - c^2 = d^2 - b^2$$

$$(a-c)(a+c) = (d-b)(d+b)$$

$$(a-c)(a+c) - (d-b)(d+b) = 0$$

So there is one pair I see:

$$a -c = d - b, a + c = d + b$$

Suppose WLOG, $a > b > c > d > 0$

But that doesnt strike anything.