Senior Kangaroo 2019 Q19

The square $ABCD$ has sides of length 105. The point $M$ is the midpoint of side $BC$. The point $N$ is the midpoint of $BM$. The lines $BD$ and $AM$ meet at the point $P$. The lines $BD$ and $AN$ meet at the point $Q$.

What is the area of triangle $APQ$?