# Strings with brackets

How many strings of length $$13$$ can be formed from $$9$$ $$1$$'s, two $$($$'s and two $$)$$'s such that

1. the substring $$(\, )$$ never occurs,
2. the first $$(\,$$ occurs before the first $$)\,$$,
3. the second $$(\,$$ occurs before the second $$)\,$$?
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