# Safety first

For a positive integer $$p$$, define the positive integer $$n$$ to be $$p$$-safe if $$n$$ differs in absolute value by more than 2 from all multiples of $$p$$. For example, the set of 10-safe numbers includes $$\{3, 4, 5, 6, 7, 13, 14, 15, 16, 17\}$$.

Find the number of positive integers less than or equal to 10 000 which are simultaneously 7-safe, 11-safe, and 13-safe.

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