Let $a_1a_2a_3a_4$ be a square, and let $a_5,a_6,a_7,\ldots, a_{34}$ be distinct points inside the square. non-intersecting segments $\overline{a_ia_j}$ are drawn for various pairs $(i, j)$ with $1\le i, j\le 34$, such that the square is dissected into triangles. assume each $a_i$ is an endpoint of at least one of the drawn segments. how many triangles are formed?