<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 is_valid(self, s):
        for i in range(len(s) - 1):
            if s[i] != "1" and s[i + 1] != "1":
                return False

        return True


    def validStrings(self, n: int) -> List[str]:
        if n == 1:
            return ["0", "1"]

        s = "0"
        for _ in range(n - 1):
            if s[-1] == "0":
                s += "1"
            else:
                s += "0"

        valid_strs = []
        num = int(s, 2)
        max_num = int("1" + ("0" * n), 2)
        print(num)
        print(max_num)
        while num < max_num:
            if self.is_valid(s):
                valid_strs.append(s)
            num += 1
            s = format(num, f'0{n}b')

        return valid_strs
        
245