<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 {
public:
    int n;
    int dp(vector<vector<int>>& dp_vec, int typed, int copied){
        if(typed > n){
            return -1;
        }
        if(typed == n){
            return 0;
        }
        if(dp_vec[typed][copied] != -2){
            return dp_vec[typed][copied];
        }
        int result = INT_MAX;
        if(copied < typed){
            int rc = dp(dp_vec, typed, typed);
            if(rc != -1){
                result = min(result, 1 + rc);
            }
        }
        if(copied > 0){
            int rc = dp(dp_vec, typed + copied, copied);
            if(rc != -1){
                result = min(result, 1 + rc);
            }
        }
        dp_vec[typed][copied] = result == INT_MAX ? -1 :result;
        return result == INT_MAX ? -1 : result;
    }
    
    int minSteps(int n) {
        vector<vector<int>> dp_vec(n, vector<int>(n, -2));
        this -> n = n;
        return dp(dp_vec, 1, 0);
    }
};
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