<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 {
    
    struct Step {
        int steps;
        int cur;
        int cop;
    };
    
public:
    int minSteps(int n) {
        Step step;
        
            
            
        step.steps = 0;
        step.cur = 1;
        step.cop = 0;
        
        queue<Step> que;
        que.push(step);
        
        while (!que.empty()) {
            step = que.front();
            que.pop();
            if (step.cur == n) {
                return step.steps;
            }
            else if (step.cur < n) {
                step.steps++;
                if (step.cur == step.cop) {
                    step.cur += step.cop;
                    que.push(step);
                }
                else if (step.cop == 0) {
                    step.cop = step.cur;
                    que.push(step);
                }
                else {
                    Step s = step;
                    s.cop = s.cur;
                    que.push(s);
                    step.cur+= step.cop;
                    que.push(step);
                }
            }
        }
        
        
        return -1;
    }
};
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