  This is the first part of the project toward proving the BCOV's Feymann graph
sum formula of all genera Gromov-Witten invariants of quintic Calabi-Yau
threefolds. In this paper, we introduce the notion of N-Mixed-Spin-P fields,
construct their moduli spaces, their virtual cycles, their virtual localization
formulas, and a vanishing result associated with irregular graphs.
