<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 {
private:
    vector<vector<int>> memo;

    bool isPrime(int number) {
        if (number < 2)
            return false;
        if (number == 2)
            return true;
        if (number % 2 == 0)
            return false;
        for (int i = 3; (i * i) <= number; i += 2) {
            if (number % i == 0)
                return false;
        }
        return true;
    }

    int fn(int n, int screen, int clip, int steps) {
        if (screen == n)
            return steps;
        if (screen > n)
            return INT_MAX;
        if (memo[screen][clip] != -1)
            return memo[screen][clip];
        // choices
        int pick = fn(n, screen + screen, screen, steps + 2);
        int npick = (clip > 0) ? fn(n, screen + clip, clip, steps + 1) : INT_MAX;
        return memo[screen][clip] = min(pick, npick);
    }

public:
    int minSteps(int n) {
        if (isPrime(n))
            return n;
        memo.assign(n + 1, vector<int>(n + 1, -1));
        return fn(n, 1, 0, 0);
    }
};

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