<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>

#include <deque>
#include <limits>
#include <algorithm>
class Solution {
struct State {
        int clipboard;
        int size;
        int moves;
    };
public:
    int minSteps(int n) {
        if (n == 1) {
            return 0;
        }
        int best_route = std::numeric_limits<int>::max();
        std::deque<State> workQueue;
        workQueue.push_back({.clipboard = 1, .size = 1, .moves = 1});
        while (workQueue.size() > 0) {
            State state = workQueue.front();
            workQueue.pop_front();
            if (state.size == n) {
                best_route = std::min(best_route, state.moves);
                continue;
            }
            if (state.size > n || state.moves >= best_route) {
                continue;
            }
            workQueue.push_back({.clipboard = state.size, .size = state.size * 2, .moves = state.moves + 2});
            workQueue.push_back({.clipboard = state.clipboard, .size = state.size + state.clipboard, .moves = state.moves + 1});
        }
        return best_route;
    }
};
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