<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:
    set<string>st;
        string op(int type,string& s){
        if(type==0){
            for(int i = 0;i<s.length();i++){
                if(s[i]=='1') s[i]='0';
                else s[i]='1';
            }
        }
        else if(type==1){
            for(int i = 1;i<s.length();i+=2){
                if(s[i]=='1') s[i]='0';
                else s[i]='1';
            }
        }
        else if(type==2){
            for(int i = 0;i<s.length();i+=2){
                if(s[i]=='1') s[i]='0';
                else s[i]='1';
            }
        }
        else{
            for(int k = 0;3*k+1<=s.length();k++){
                int i = 3*k;
                if(s[i]=='1') s[i]='0';
                else s[i]='1';
            }
        }
        return s;
    }
    void solve(string s,int presses,unordered_map<string,unordered_map<int,int>>&dp){
        if(presses == 0){
            st.insert(s);
            return;
        }

        if(dp.count(s) and dp[s].count(presses)) return;

        dp[s][presses] = 1;
     
        solve(op(0,s),presses-1,dp); 
        solve(op(1,s),presses-1,dp); 
        solve(op(2,s),presses-1,dp); 
        solve(op(3,s),presses-1,dp); 
    }
    int flipLights(int n, int presses) {
        string s(n,'1');
        unordered_map<string,unordered_map<int,int>>dp;
        solve(s,presses,dp);
        return st.size();       
    }
};
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