A bee starts flying from point $P_0$. She flies 1 inch due east to point $P_1$. For $j\ge 1$, once the bee reaches point $P_j$, she turns $30^{\circ }$ counterclockwise and then flies $j+1$ inches straight to point $P_{j+1}$. When the bee reaches $P_{2027}$ she is exactly $a\sqrt{b}+c\sqrt{d}$ inches away from $P_0$ where $a,b,c,$ and $d$ are positive integers and $b$ and $d$ are not divisible by the square of any prime. What is $a+b+c+d$?