<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 isValid(string ip) {
        for(int i=0; i<ip.size(); i++) {
            if(ip[i] == '.') {
                ip[i] = ' ';
            }
        }
        stringstream ss(ip);
        vector<string> nums;
        string num;
        while(ss >> num) {
            nums.push_back(num);
            if(num.length()>3) {
                return false;
            }
        }
        if(nums.size() != 4) {
            return false;
        }

        for(string num : nums) {
            if(num.size() != 1 && num[0] == '0') {
                return false;
            }
            int n = stoi(num);
            if(n > 255) {
                return false;
            }
        }

        return true;
    }

    vector<string> restoreIpAddresses(string s) {
        vector<string> ans;
        int n = s.length();
        if(n < 4) {
            return ans;
        }
        vector<int> perm(n);
        for(int i=1; i<=3; i++) {
            perm[n-i] = 1;
        }
        sort(perm.begin(), perm.end());
        do {
            string ip = "";
            for(int i=0; i<s.size(); i++) {
                ip += s[i];
                if(perm[i]) {
                    ip += ".";
                }
            }
            if(isValid(ip)) {
                ans.push_back(ip);
            }
        }while(next_permutation(perm.begin(), perm.end()));
        return ans;
    }
};
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