Functions

If \(S=\{a \in \mathbf{R}:|2 a-1|=3[a]+2\{a \}\}\), where \([t]\) denotes the greatest integer less than or equal to \(t\) and \(\{t\}\) represents the fractional part of \(t\), then \(72 \sum_\limits{a \in S} a\) is equal to _________.