<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 xorStrings(string s1, const string& s2) {
        int n = s1.size();
        for (int i = 0; i < n; i++) {
            s1[i] = (s1[i] == s2[i]) ? '0' : '1';
        }
        return s1;
    }

    void bulb(string s, vector<string>& v, int rem, unordered_map<string, unordered_map<int, int>>& dp) {
        if (rem < 0) return;
        if (dp.count(s) && dp[s].count(rem)) return;
        dp[s][rem] = 1;

        if (rem == 0) {
            st.insert(s);
            return;
        }

        bulb(xorStrings(s, v[0]), v, rem - 1, dp);
        bulb(xorStrings(s, v[1]), v, rem - 1, dp);
        bulb(xorStrings(s, v[2]), v, rem - 1, dp);
        bulb(xorStrings(s, v[3]), v, rem - 1, dp);
    }

    int flipLights(int n, int presses) {
        string b1, b2, b3, b4;
        for (int i = 0; i < n; i++) {
            if (i % 2 == 0) {
                b1 += '1';
                b3 += '1';
                b2 += '0';
            } else {
                b1 += '1';
                b3 += '0';
                b2 += '1';
            }
        }
        for (int i = 0; i < n; i++) {
            if (i % 3 == 0) {
                b4 += '1';
            } else {
                b4 += '0';
            }
        }

        vector<string> v = {b1, b2, b3, b4};
        string init(n, '1');
        unordered_map<string, unordered_map<int, int>> dp;

        bulb(init, v, presses, dp);
        return st.size();
    }
};

167200