I'm trying to figure out a way to perform the following loop on a remote host via ssh.

Basically it renames a series of directories to create a rotating backup. But it's local. I want it to work against directories on a remote host.

while [ $n -gt 0 ];
    do {
    src=$(($n-1))
    dst=$n
    if [ -d /backup/$src ];
    then {
    mv /backup/$src /backup/$dst;
    }
    fi;
    }
    ((n--))
done;