<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 = [{} for _ in range(n + 1)]
        def _minSteps(start, num):
            # if start == 0:
            #     memo[1][1] = 1
            if start == n:
                memo[start][num] = 0
                return memo[start][num]
            if start >= n:
                return n * 10
            if memo[start].get(num) is not None:
                return memo[start][num]
            # copy
            steps = n * 10
            if start > num:
                steps = _minSteps(start, start)
                steps += 1
            # paste
            pasteStep = n * 10
            if num != 0:
                pasteStep = _minSteps(start + num, num)
                pasteStep += 1
            memo[start][num] = min(steps, pasteStep)
            return memo[start][num]
        # memo[0][1] = 0
        _minSteps(1, 0)
        return memo[1][0]
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