\[ \large 1 \, \square \, \dfrac12 \, \square \, \dfrac13 \, \square \, \dfrac14 \, \square \,\dfrac15 \, \square \, \cdots \square \, \dfrac1{31} =\dfrac1{32} \]

There are \( 2^{30} \) ways in which we can fill the squares with the mathematical operators \( +\) and \(-\).

How many ways would make the equation true?

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