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?