<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:
        cache = dict()
        currMin = n
        def do(numCopied, currNum, numOps):
            nonlocal cache
            nonlocal currMin
            if (numCopied, currNum) in cache:
                return cache[(numCopied, currNum)]
            if numOps >= currMin:
                return n
            if currNum == n:
                cache[(numCopied, currNum)] = numOps
                currMin = min(currMin, numOps)
                return numOps
            copy = n
            if numCopied < currNum and currNum + numCopied <= n:
                copy = do(currNum, currNum, numOps + 1)
            paste = n
            if currNum + numCopied <= n:
                paste = do(numCopied, currNum + numCopied, numOps + 1)
            cache[(numCopied, currNum)] = min(copy, paste)
            return min(copy, paste)
        do(0, 1, 0)
        return cache[(0, 1)]
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