Let S be the set of real numbers \( c \in (0,1] \) with the property: \( \forall \) continuous functions \( f : [0,1] \to \mathbb{R} \) with \( f(0) = f(1) \) exists a \( x \in [0,1] \) , so that also \( x+c \in [0,1] \) and \( f(x) = f(x+c) \)

Let \( a \) bet the sum of all elements \( z \) in \( S \) with \( z \ge \frac{1}{10} \)

The answer to type in is: \( 2520 * a \)

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