<p>There is a room with <code>n</code> bulbs labeled from <code>1</code> to <code>n</code> that all are turned on initially, and <strong>four buttons</strong> on the wall. Each of the four buttons has a different functionality where:</p>

<ul>
	<li><strong>Button 1:</strong> Flips the status of all the bulbs.</li>
	<li><strong>Button 2:</strong> Flips the status of all the bulbs with even labels (i.e., <code>2, 4, ...</code>).</li>
	<li><strong>Button 3:</strong> Flips the status of all the bulbs with odd labels (i.e., <code>1, 3, ...</code>).</li>
	<li><strong>Button 4:</strong> Flips the status of all the bulbs with a label <code>j = 3k + 1</code> where <code>k = 0, 1, 2, ...</code> (i.e., <code>1, 4, 7, 10, ...</code>).</li>
</ul>

<p>You must make <strong>exactly</strong> <code>presses</code> button presses in total. For each press, you may pick <strong>any</strong> of the four buttons to press.</p>

<p>Given the two integers <code>n</code> and <code>presses</code>, return <em>the number of <strong>different possible statuses</strong> after performing all </em><code>presses</code><em> button presses</em>.</p>

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

<pre>
<strong>Input:</strong> n = 1, presses = 1
<strong>Output:</strong> 2
<strong>Explanation:</strong> Status can be:
- [off] by pressing button 1
- [on] by pressing button 2
</pre>

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

<pre>
<strong>Input:</strong> n = 2, presses = 1
<strong>Output:</strong> 3
<strong>Explanation:</strong> Status can be:
- [off, off] by pressing button 1
- [on, off] by pressing button 2
- [off, on] by pressing button 3
</pre>

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

<pre>
<strong>Input:</strong> n = 3, presses = 1
<strong>Output:</strong> 4
<strong>Explanation:</strong> Status can be:
- [off, off, off] by pressing button 1
- [off, on, off] by pressing button 2
- [on, off, on] by pressing button 3
- [off, on, on] by pressing button 4
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
	<li><code>0 &lt;= presses &lt;= 1000</code></li>
</ul>

class Solution {
public:
    void solve(string & str , int presses , int n , set<string> & st ,map<pair<string,int>,bool> & dp){

        if(presses == 0) {
            st.insert(str);
            return;
        }

        string ns = str;
        
        for(int i =0 ; i < n ; i++){
            if(ns[i] == '0'){
                ns[i] = '1';
            }else{
                ns[i] = '0';
            }
        }
        if(dp[{ns,presses}] == false){
            solve(ns,presses-1,n,st,dp);
            dp[{ns,presses}] = true;
        }
        ns = str;


        for(int i =0 ; i < n ; i+=2){
            if(ns[i] == '0'){
                ns[i] = '1';
            }else{
                ns[i] = '0';
            }
        }
        
        if(dp[{ns,presses}] == false){
            solve(ns,presses-1,n,st,dp);
            dp[{ns,presses}] = true;
        }
        ns = str;

        for(int i =1 ; i < n ; i+=2){
            if(ns[i] == '0'){
                ns[i] = '1';
            }else{
                ns[i] = '0';
            }
        }
        
        if(dp[{ns,presses}] == false){
            solve(ns,presses-1,n,st,dp);
            dp[{ns,presses}] = true;
        }
        ns = str;

        for(int i =0 ; i < n ; i+=3){
            if(ns[i] == '0'){
                ns[i] = '1';
            }else{
                ns[i] = '0';
            }
        }
        
        if(dp[{ns,presses}] == false){
            solve(ns,presses-1,n,st,dp);
            dp[{ns,presses}] = true;
        }
        ns = str;

    }
    int flipLights(int n, int presses) {
     string str = "";
     if(presses == 0) return 1;
     for(int i =0 ; i < n ; i++){
         str+='1';
     }   
     set<string> st;
     map<pair<string,int>,bool> dp;
     solve(str,presses,n,st,dp);

     for(auto it : st){
         cout << it << endl;
     }

     return st.size();

    }
};
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