2 Keys Keyboard
<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>
Math; Dynamic Programming
class Solution {
    private int[] f;

    public int minSteps(int n) {
        f = new int[n + 1];
        Arrays.fill(f, -1);
        return dfs(n);
    }

    private int dfs(int n) {
        if (n == 1) {
            return 0;
        }
        if (f[n] != -1) {
            return f[n];
        }
        int ans = n;
        for (int i = 2; i * i <= n; ++i) {
            if (n % i == 0) {
                ans = Math.min(ans, dfs(n / i) + i);
            }
        }
        f[n] = ans;
        return ans;
    }
}