Horse-Racing Duals BASH NC

read N
touch list      # create file named list
for (( i=0; i<N; i++ )); do
    read Pi     # store in Pi
    echo $Pi >> list    # append to file list
done
sort -n list > sorted   # sort file list and create file sorted

minimum=99999999
distance=0
previous=0
first=$(head -n 1 sorted)   # first horse from sorted

for i in $(cat sorted); do  # iterate through lines from sorted
    if [ $i != $first ]; then
        let "distance=i-previous"   # calculate distance
        # Since list is sorted i know that distance is always >= 0
        if [ $distance -lt $minimum ]; then
            let "minimum=distance"      # store minimal distance
        fi
        let "previous=i"    # current i horse becomes previous
    else
        let "previous=i"    # first horse becomes previous
    fi
 done

echo "$minimum"     # print minimum