<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:
        memo = {}

        def helper(steps, clip, pattern):
            # Base cases
            if len(pattern) == n:
                return steps
            if len(pattern) > n or steps > n:
                return float('inf')
            
            # Memoization check
            key = (len(pattern), len(clip))
            if key in memo:
                return memo[key]

            # Recursive calls
            # Option 1: Copy all and paste
            copy_paste = helper(steps + 2, pattern, pattern + pattern)
            # Option 2: Paste clipboard content
            paste = float('inf')
            if clip:
                paste = helper(steps + 1, clip, pattern + clip)

            # Store result in memo and return
            memo[key] = min(copy_paste, paste)
            return memo[key]

        # Start with 0 steps, empty clipboard, and "A" as the initial pattern
        return helper(0, '', 'A')

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