<p>There is only one character <code>&#39;A&#39;</code> on the screen of a notepad. You can perform one of two operations on this notepad for each step:</p>

<ul>
	<li>Copy All: You can copy all the characters present on the screen (a partial copy is not allowed).</li>
	<li>Paste: You can paste the characters which are copied last time.</li>
</ul>

<p>Given an integer <code>n</code>, return <em>the minimum number of operations to get the character</em> <code>&#39;A&#39;</code> <em>exactly</em> <code>n</code> <em>times on the screen</em>.</p>

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

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 3
<strong>Explanation:</strong> Initially, we have one character &#39;A&#39;.
In step 1, we use Copy All operation.
In step 2, we use Paste operation to get &#39;AA&#39;.
In step 3, we use Paste operation to get &#39;AAA&#39;.
</pre>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 0
</pre>

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

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

class Solution {
public:
    int minSteps(int n) {
        if (n == 1)
            return 0;

        set<pair<int, int>> toolatebruh;
        queue<pair<int, int>> q; // {scene, buffer}
        q.push({1, 1});
        for (int ans = 1; q.size(); ans++)
            for (int x = q.size(); x; x--) {
                int scene = q.front().first;
                int buffer = q.front().second;
                q.pop();

                if (scene == n) // height of tree is ans
                    return ans;
                if (scene + buffer > n) // no longer possible
                    continue;
                if (toolatebruh.count({scene, buffer}))
                    continue;
                toolatebruh.insert({scene, buffer});

                if (scene == buffer) // only paste possible
                    q.push({2 * scene, scene});
                else {
                    q.push({scene, scene});           // copy
                    q.push({scene + buffer, buffer}); // paste
                }
            }
        return -1;
    }
};
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