A bug is walking on an infinite $2$D grid. He starts at some location $($i$,$ j$)$ sum N$^2$ in the first quadrant, and is constrained to stay in the first quadrant $($say$,$ by walls along the x and y axes$).$ Every second he does one of the following $($if possible$)$:Jump one inch down, to $($i$,$ j$-1).$Jump one inch left, to $($i $-1,$ j$).$For example, if he is at $(5,0),$ his only option is to jump left to $(4,0).$Prove that no matter how he jumps, he will always reach $(0,0)$ in finite time.