<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 {
public:
    bool verify(string aux){
        
        int len = aux.length();

        int num = stoi(aux);

        if(len > 3 || num > 255 || (len == 3 && num < 100) || (len == 2 && num < 10)){
            return false;
        }

        return true;
    }

    bool check(string aux){
        
        if(aux[aux.length()-1] == '.' || aux[0] == '.'){
            return false;
        }

        int start = 0;

        int index = 0;

        while(index < aux.length()){
            if(aux[index] == '.'){
                if(!verify(aux.substr(start,index-start))){
                    return false;
                }
                start = index+1;
            }
            index++;
        }

        if(!verify(aux.substr(start,index-start))){
            return false;
        }

        return true;

    }

    void solve(vector<string>&ans,string aux,string s,int index){
        
        if(aux.length() > s.length()+3){
            return;
        }

        if(aux.length() == s.length()+3 && index == s.length()){
            if(check(aux)){
                ans.push_back(aux);
            }
            return;
        }

        aux.push_back(s[index]);

        aux.push_back('.');

        solve(ans,aux,s,index+1);

        aux.pop_back();

        solve(ans,aux,s,index+1);

        return;

    }
    vector<string> restoreIpAddresses(string s) {
        
        if(s.length() > 12){
            return {};
        }
        
        vector<string>ans;

        string aux;

        solve(ans,aux,s,0);

        return ans;
    }
};
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