<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:
    def minSteps(self, n: int) -> int:
        # n = 1 ans = 0
        # n = 2 ans = 2
        # n = 3 ans = 3
        # n = 4 ans = 4
        # n = 5 ans = 5 
        # n = 6 ans = 5
        if n == 1:
            return 0
        self.target_length = n
        memo = {}
        def find_min_steps(current_length: int, clipboard_length: int) -> int:
            if (current_length, clipboard_length) in memo:
                return memo[(current_length, clipboard_length)]
            elif current_length == self.target_length:
                return 0
            elif current_length > self.target_length:
                return float('inf')
            copy_and_paste = 2 + find_min_steps(current_length * 2,\
                                                current_length)
            paste_only = 1 + find_min_steps(current_length + clipboard_length,\
                                            clipboard_length)
            memo[(current_length, clipboard_length)] = min(copy_and_paste, paste_only)
            return min(copy_and_paste, paste_only)
        return 1 + find_min_steps(1, 1)

27841