(M_{R}^{-1})^{ij}(m_{D}^{T})^{jb} \, + 
\, \text{higher order terms}
\label{seesaw}\end{aligned}$$ The expression for the full diagonalizing matrix was first given in [@Schechter:1981cv]. The light neutrino mass matrix in is further diagonalized by a unitary matrix $U_\nu$ in the light neutrino sector $\nu^a$; $a = 1,2,3$. This is the famous type-I seesaw formula linking the smallness of the light neutrinos to the heaviness of the right-handed neutrinos $\nu_R$. Depending on the value of “n” many possibilities can be envisaged. For example, first consider n$\leq$3 of “high-scale” constructions. Current experimental and cosmological observations indicate that the neutrino masses are $\nu^a_m \leq \mathcal{O} (0.1)$ eV [@Aghanim:2018eyx; @deSalas:2018bym] with recent Planck data indicating that sum of neutrino masses $\sum_a\nu^a_m = 0.23$ eV [@Lattanzi:2017ubx]. Hence, for “sizeable” Yukawa coupling, $Y_{\nu}\sim\mathcal{O}(1)$, in order to satisfy the neutrino mass bound, heavy neutrino mass $M_{N}$ will be order of $\mathcal{O}(10^{14}\,\text{GeV})$. This characterizes the case of genuine “high-scale” seesaw constructions. For n=2 one has the minimal realistic scenario in which two small neutrino masses arise naturally at the tree-level [@Schechter:1980gr]. These will be identified with the “atmospheric scale” and the “solar” mass scales. The case n=1 leads the minimal prescription that generates only one small neutrino mass at the tree level 