<p>A <strong>valid IP address</strong> consists of exactly four integers separated by single dots. Each integer is between <code>0</code> and <code>255</code> (<strong>inclusive</strong>) and cannot have leading zeros.</p>

<ul>
	<li>For example, <code>&quot;0.1.2.201&quot;</code> and <code>&quot;192.168.1.1&quot;</code> are <strong>valid</strong> IP addresses, but <code>&quot;0.011.255.245&quot;</code>, <code>&quot;192.168.1.312&quot;</code> and <code>&quot;192.168@1.1&quot;</code> are <strong>invalid</strong> IP addresses.</li>
</ul>

<p>Given a string <code>s</code> containing only digits, return <em>all possible valid IP addresses that can be formed by inserting dots into </em><code>s</code>. You are <strong>not</strong> allowed to reorder or remove any digits in <code>s</code>. You may return the valid IP addresses in <strong>any</strong> order.</p>

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

<pre>
<strong>Input:</strong> s = &quot;25525511135&quot;
<strong>Output:</strong> [&quot;255.255.11.135&quot;,&quot;255.255.111.35&quot;]
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;0000&quot;
<strong>Output:</strong> [&quot;0.0.0.0&quot;]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;101023&quot;
<strong>Output:</strong> [&quot;1.0.10.23&quot;,&quot;1.0.102.3&quot;,&quot;10.1.0.23&quot;,&quot;10.10.2.3&quot;,&quot;101.0.2.3&quot;]
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 20</code></li>
	<li><code>s</code> consists of digits only.</li>
</ul>

class Solution:
    def backtrack(self,dot,current,remain):
        if dot==0 and len(remain)>0:
            if len(remain)>1 and remain[0]=='0': return
            if int(remain)<=255:
                self.out.append(current+'.'+remain)
            return

        maxlen = min(3,len(remain))
        if dot==3:
            tmp = ""
            for i in range(maxlen):
                tmp+=remain[i]
                if len(tmp)>1 and tmp[0]=='0': continue
                if int(tmp)<=255:
                    self.backtrack(2,tmp,remain[i+1:])
        else:
            tmp = ""
            for i in range(maxlen):
                tmp+=remain[i]
                if len(tmp)>1 and tmp[0]=='0': continue
                if int(tmp)<=255:
                    self.backtrack(dot-1,current+'.'+tmp,remain[i+1:])
        return


    def restoreIpAddresses(self, s: str) -> List[str]:
        self.out = []
        self.backtrack(3,"",s)
        return self.out
16400