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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