A insects initially at origin has to move from `(0,0)` to `(6,6)`. It moves towards +ve x-axis or +ve y-axis. In each step it moves from `(x,y)` to `(x+1,y)` or `(x,y+1)`. Find the number of different paths it can follow to complete it's journey if it does not pass through any of the four points `(3,1),(3,2),(4,1)` and `(4,2)`.

Answer

`469`