Let G be a hypercube on n bits. For vertices u$,$ v in $\{0,1\}^$n$,$ bit$-$fixing scheme decides a path from u v by scanning the bit strings corresponding to u and v from the most significant bit to the least significant bit and flips the individual bits in order. That is$,$ correct the mismatched bits in order.

Now consider the following variant of the bit$-$fixing scheme. Each packet pv $($for v in $\{0,1\}^$ n$)$ randomly orders the position of bits in the string of its source v and corrects the mismatched bits in order $($of this new random string$).$ Show that there is a permutation for which with high probability this algorithm requires $2^($n$)$ steps to complete the routing.