A lawn sprinkling system is controlled automatically by a certain combination of the following variables.

i) Season, $S$ ( $S = 1$ if summer, $S = 0$ if any other season),
ii) Moisture content of soil, $M$ ( $M = 1$ if moisture content is high, $M = 0$ if low),
iii) Outside temperature, $T$ ( $T = 1$ if temperature is high, $T = 0$ if low), and
iv) Outside humidity, $H$ ( $H = 1$ if humidity is high, $H = 0$ if low).

The sprinkler should turn on under any of the following circumstances.

i) The moisture content is low in winter.
ii) The temperature is high, and the moisture content is low in summer.
iii) The temperature is high, and the humidity is high in summer.
iv) The temperature is low, and the moisture content is low in summer.
v) The temperature is high, and the humidity is low in all seasons.

Design the simplest possible logic circuit involving the variables $S$ , $M$ , $T$ , and $H$ for turning on the sprinkler system, using only 2 or 3 input NAND gates.