The solid that require the greatest energy input to melt by mass is the option;
Covalent network
Solution Explanation
The elementary particles of a solid are held together by bonds that require an input of energy to unlock, and once broken, the particles are then able to change location within their containing vessels with less restrictions
Polar covalent molecular solids have the following characteristics;
a) Soluble in water b) Low melting point, b) Conduct electricity
Solids that are made up of a covalent network have the following characteristics
a) High melting point temperature b) Non conductive of electricity c) Not soluble in water
Solids of ionic compounds have the following characteristics;
a) High melting point temperature b) The liquid state and solution conducts electricity c) Soluble in water
Solids that have nonpolar covalent bonds have;
a) Low melting point b) Normally in the gaseous or liquid state b) Not water soluble
The covalent network, and the solids ionic compounds require the most energy to melt, however, the strength of the ionic bond in an ionic compound is a factor the charges present and the sizes of the atom, while the covalent network solid, are combined to <em>form essentially as a single molecule</em> and therefore require the greatest heat energy input to melt
, with 
in our case.