It turns out that $12\mathrm{cm}$ is the smallest length of wire that can be bent to form an integer sided right angle triangle in exactly one way, but there are many more examples.

• $\mathbf{12}\mathbf{cm}$: $(3,4,5)$
• $\mathbf{24}\mathbf{cm}$: $(6,8,10)$
• $\mathbf{30}\mathbf{cm}$: $(5,12,13)$
• $\mathbf{36}\mathbf{cm}$: $(9,12,15)$
• $\mathbf{40}\mathbf{cm}$: $(8,15,17)$
• $\mathbf{48}\mathbf{cm}$: $(12,16,20)$

In contrast, some lengths of wire, like $20\mathrm{cm}$, cannot be bent to form an integer sided right angle triangle, and other lengths allow more than one solution to be found; for example, using $120\mathrm{cm}$ it is possible to form exactly three different integer sided right angle triangles.

• $\mathbf{120}\mathbf{cm}$: $(30,40,50)$, $(20,48,52)$, $(24,45,51)$

Given that $L$ is the length of the wire, for how many values of $L\le 1500000$ can exactly one integer sided right angle triangle be formed?