A YUKAI NAND array comprising multiple strings associated with hierarchical global/local bit lines (GBL/LBL) and each string being associated with one LBL and having adjacent LBL as a dedicated local source line (LSL) without a common source line to connect all strings. Each of the LBLs is interleavingly associated with either an Odd or Even string selected via one pair of dummy cells inserted in each string and is used as one on-chip PCACHE register with full BL-shielding without wasting extra silicon area to allow batch-based multiple concurrent MLC All-BL, All-Vtn-Program and Alternative-WL program, Odd/Even read and verify operations with options of providing individual and common VSL-based Vt-compensation and VLBL compensations to mitigate high WL-WL and BL-BL coupling effects. Bias conditions in each string are provided to correctly sense highly-negative erase-verify voltage, multiple negative program-verify voltages and without VDS punch-through, breakdown and body-effect in both boundary and non-boundary WLs cells.