The nucleus of an atom consists of protons and neutrons $($no electrons$).$ A nucleus of a carbon$-12$ isotope contains six protons and six neutrons, while a nitrogen$-14$ nucleus comprises seven protons and seven neutrons.

A graduate student performs a nuclear physics experiment in which she bombards nitrogen$-14$ nuclei with very high speed carbon$-12$ nuclei emerging from a particle accelerator. As a result of each such collision, the two nuclei disintegrate completely, and a mix of different particles are emitted, including electrons, protons, antiprotons $($with electric charge $-e$ each$),$ positrons $($with charge $+e$ each$),$ and various neutral particles $($including neutrons and neutrinos$).$

For a particular collision, she detects the emitted products and find $17$ protons, $4$ antiprotons, $8$ positrons, and $23$ neutral particles.

How many $N$ electrons are also emitted?