In the classic "Crossing Ladders" problem, we are given the lengths $x$ and $y$ of two ladders resting on the opposite walls of a narrow, level street. We are also given the height $h$ above the street where the two ladders cross and we are asked to find the width of the street ($w$).

Here, we are only concerned with instances where all four variables are positive integers.
For example, if $x=70$, $y=119$ and $h=30$, we can calculate that $w=56$.

In fact, for integer values $x$, $y$, $h$ and $0<x<y<200$, there are only five triplets $(x,y,h)$ producing integer solutions for $w$:
$(70,119,30)$, $(74,182,21)$, $(87,105,35)$, $(100,116,35)$ and $(119,175,40)$.

For integer values $x,y,h$ and $0<x<y<1000000$, how many triplets $(x,y,h)$ produce integer solutions for $w$?