There are $7$ switches on a switchboard, some of which are on and some of which are off. In one move, you pick any $2$ switches and toggle each of them-if the switch you pick is currently off, you turn it on, if it is on, you turn it off. Your aim is to execute a sequence of moves and turn all $7$ switches on. For which of the following initial configurations is this not possible? Each configuration lists the initial positions of the $7$ switches in sequence, from switch $1$ to switch $7.$
- (off,on,off,on,off,off,on)
- (off,on,on,on,on,on,off)
- (on,off,on,on,on,on,on)
- (off,off,off,off,off,on,off)