<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;
        }
        
        auto q = std::queue<std::tuple<int, int, int>>();
        q.emplace(1, 1, 1);

        while (not q.empty()) {
            const auto [num, steps, copied] = q.front(); q.pop();

            if (num >= n) {
                if (num == n) {
                    return steps;
                }
                continue;
            }

            q.emplace(num + copied, steps + 1, copied);
            if (num > copied) {
                q.emplace(num, steps + 1, num);
            }
        }

        return -1;
    }
};

/*
    let dp(i) = minimum number of operations to get the character 'A' exactly `i` times

    n = 6
    copy  <- A 
    paste -> AA
    paste -> AAA
    copy  <- AAA
    paste -> AAA AAA

    n = 9
    copy  <- A 
    paste -> AA
    paste -> AAA
    copy  <- AAA
    paste -> AAA AAA
    paste -> AAA AAA AAA

    n = 7
    copy  <- A
    paste -> AA
    paste -> AAA
    paste -> AAAA
    paste -> AAAAA
    paste -> AAAAAA
    paste -> AAAAAAA

    n = 10
    copy  <- A
    paste -> AA
    copy  <- AA
    paste -> AA AA
    paste -> AA AA AA
    paste -> AA AA AA AA 
    paste -> AA AA AA AA AA

    n = 49
    copy  <- 1 
    paste -> 2
    paste -> 3


    copy  <- 2
    paste -> 4
    copy  <- 4
    paste -> 8
    copy  <- 8 
    paste -> 16
    paste -> 32
    paste -> 48

    


*/ 

69954