<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:
    string performa(string s, int operation) {
        string p = s;
        // cout << s << endl;
        int n = s.size();
        int start;
        int incrementor;
        if (operation == 1) {
            start = 0;
            incrementor = 1;
        } else if(operation == 2) {
            start = 1;
            incrementor = 2;

        } else if(operation == 3) {
            start = 0;
            incrementor = 2;

        } else {
            start = 0;
            incrementor = 3;
        }
        // cout << start << " " << incrementor << endl;
        for(int i = start; i < n; i+=incrementor) {
                if (s[i] == '0') {
                    p[i] = '1';
                } else {
                    p[i] ='0';
                }
        }
        // cout << p << endl;

        return p;
    
    
    } 
    int flipLights(int n, int presses) {

        set<string> vis;
        string s = "";
        for(int i = 0; i<n;i++) s+="1";
        int ans = 0;
        if (presses==0) return 1;
        int count = 0;
        queue<string> q;
        q.push(s);
        while(!q.empty()) {
            int sz = q.size();
            if (count == presses) break;
            vis.clear();
            for(int ii =0; ii < sz; ii++) {
                string p = q.front();
                q.pop();
                // if (p.second == 0) continue;
                // int used = 0;
                for (int i = 1; i<=4; i++) {
                    string x = performa(p, i);
                    // cout << x << endl;
                    // cout << "origin :" << p << " opera : " << i << " chna : " << x << endl;   
                    if (vis.find(x) == vis.end()) {
                        // cout << x << endl;
                        q.push(x);
                        // used = 1;
                        // presses = presses-1;
                        // ans+=1;
                        vis.insert(x);
                    } 
                }
            }

            if (q.size() == sz) return sz;
            count++;
            // presses = used == 1 ? presses-1 : presses;
            
        }

        return q.size();
        
    }
};
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