<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:
   map<vector<bool>,map<int,int>> mp2;
    int flipLights(int n, int presses) {
        vector<bool> v;
        for(int i =1;i<=n;i++){
            v.push_back(true);
        }
        return m(v,presses);
    }
    map<vector<bool>,int> mp;
    int m(vector<bool>& v,int i){
        int g = 0;
        if(i == 0 ){
            if(mp[v] != 0){
                return 0;
            }
            mp[v]++;
            return 1;
        }
        if(mp2[v].count(i)){
            return 0;
        }
        vector<bool> v1 = s1(v);
         vector<bool> v2= s2(v);
          vector<bool> v3 = s3(v);
        vector<bool> v4 = s4(v);
        g +=m(v1,i-1);
        g +=m(v2,i-1);
        g +=m(v3,i-1); 
        g +=m(v4,i-1);
        return mp2[v][i] = g;

    }
    vector<bool> s1(vector<bool> v){
        for(int i = 0;i<v.size();i++){
            v[i] = !v[i];
        }
        return v;
    }
    vector<bool> s2(vector<bool> v){
         for(int i = 0;i<v.size();i+=2){
            v[i] = !v[i];
        }
        return v;
    }
    vector<bool> s3(vector<bool> v){
        for(int i = 0;i<v.size();i+=3){
            v[i] = !v[i];
        }
        return v;
    }
    vector<bool> s4(vector<bool> v){
         for(int i = 1;i<v.size();i+=2){
            v[i] = !v[i];
        }
        return v;
    }
};
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