<p>You are given a positive integer <code>n</code>.</p>

<p>A binary string <code>x</code> is <strong>valid</strong> if all <span data-keyword="substring-nonempty">substrings</span> of <code>x</code> of length 2 contain <strong>at least</strong> one <code>&quot;1&quot;</code>.</p>

<p>Return all <strong>valid</strong> strings with length <code>n</code><strong>, </strong>in <em>any</em> order.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 3</span></p>

<p><strong>Output:</strong> <span class="example-io">[&quot;010&quot;,&quot;011&quot;,&quot;101&quot;,&quot;110&quot;,&quot;111&quot;]</span></p>

<p><strong>Explanation:</strong></p>

<p>The valid strings of length 3 are: <code>&quot;010&quot;</code>, <code>&quot;011&quot;</code>, <code>&quot;101&quot;</code>, <code>&quot;110&quot;</code>, and <code>&quot;111&quot;</code>.</p>
</div>

<p><strong class="example">Example 2:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 1</span></p>

<p><strong>Output:</strong> <span class="example-io">[&quot;0&quot;,&quot;1&quot;]</span></p>

<p><strong>Explanation:</strong></p>

<p>The valid strings of length 1 are: <code>&quot;0&quot;</code> and <code>&quot;1&quot;</code>.</p>
</div>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 18</code></li>
</ul>

class Solution:
    def validStrings(self, n: int) -> List[str]:
        if n == 1:
            return ["0", "1"] 
        
        def generate_binary(numb):
            if numb == 1:
                return ["0", "1"]
            else:
                res = generate_binary(numb-1)
                res_list = []
                for num in res:
                    res_list.extend([num+"0", num+"1"])
                return res_list
        output_list =  generate_binary(n)
        final_list = list()

        for item in output_list:
            flag_valid = True
            for index in range(len(item)-1):
                if item[index] != '1' and item[index+1] != '1':
                    flag_valid = False
                    break
            if flag_valid:
                final_list.append(item)
        return final_list
        


                    

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