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Generate Binary Strings Without Adjacent Zeros

You are given a positive integer n.

You are given a positive integer n.

A binary string x is valid if all substrings of x of length 2 contain at least one "1".

Return all valid strings with length n, in any order.

Example 1

Input: n = 3

Output: ["010","011","10^1","110","111"]

Explanation: The valid strings of length 3 are: "010" , "011" , "10^1" , "110" , and "111" .

Example 2

Input: n = 1

Output: ["0","1"]

Explanation: The valid strings of length 1 are: "0" and "1" .

Constraints

  • 1 <= n <= 18

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