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Stacked (NbN/TiNx)N/NbN (N = 2, 3, 4, 5 and 10) Josephson junctions and their arrays have been fabricated on a Si chip and their microwave-induced characteristics were measured at a temperature around 10 K. To achieve a vertical and smooth edge of an NbN - TiNx multilayer, an inductively coupled plasma reactive ion etching (ICP-RIE) technique was used. Current-voltage characteristics measured for stacks of (NbN/TiNx)N/NbN Josephson junctions without microwave indicated that critical currents for those junctions distribute in a certain range. We defined Ic - spread as (Ic MAX - Ic MIN)/Ic Average to measure the distribution of Ic. The Ic - spread was minimized when the thickness of intermediate electrodes was d = 50 nm. We also evaluated values of Ic - spread for stacks prepared at different fabrication runs as a function of the number of junctions in a stack N. As a result, we found N = 3 is the maximum for practical use. For arrays, we obtained a constant-voltage step height of about 2 m A for 2 048 stacks of double-barrier junctions (N = 2), and about 1 mA for 1 024 stacks of triple-barrier junctions (N = 3).