The sequence of triangle numbers is generated by adding the natural numbers. So the $7$^th triangle number would be $1+2+3+4+5+6+7=28$. The first ten terms would be: $$1,3,6,10,15,21,28,36,45,55,\dots$$

Let us list the factors of the first seven triangle numbers:

$$\begin{array}{rl}\mathbf{1}& :1\\ \mathbf{3}& :1,3\\ \mathbf{6}& :1,2,3,6\\ \mathbf{10}& :1,2,5,10\\ \mathbf{15}& :1,3,5,15\\ \mathbf{21}& :1,3,7,21\\ \mathbf{28}& :1,2,4,7,14,28\end{array}$$

We can see that $28$ is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?