$($Bitcoin mining$)$ Josh is mining bitcoins where the process uses a $256-$bit secure hash algorithm $($SHA$-256).$ That is$,$ the hashing operation maps a digital input file of any size to a fixed $256-$bit hash value that is used as a fingerprint for that file. Show that the value of n for which the probability of at least $2$ different files being hashed to the same value exceeds $0\mathrm{.}5$ is n $1\mathrm{.}4$N$,$ where N $=2$ to the power of $256$