<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 {
    int solveRec(int n , int curr ,int copy){
        if(curr ==n ) return 0 ;
        if(curr >n) return INT_MAX/2 ;
        int o1 = INT_MAX , o2 =INT_MAX;
        if(copy!=0){
            o1 = 1+solveRec(n,curr+copy,copy);
        }

        copy = curr ;
        o2 = 2+solveRec(n,curr+copy,copy);

        return min(o1 , o2);
    }

    int solveMem(int n , int curr , int copy , vector<vector<int>>& dp){
        if(curr ==n ) return 0 ;
        if(curr >n) return INT_MAX/2 ;

        if(dp[curr][copy] != -1) return dp[curr][copy] ;
        int o1 = INT_MAX , o2 =INT_MAX;
        if(copy!=0){
            o1 = 1+solveMem(n,curr+copy,copy,dp);
        }

        copy = curr ;
        o2 = 2+solveMem(n,curr+copy,copy,dp);

        return dp[curr][copy] = min(o1 , o2);
    }
public:
    int minSteps(int n) {
        // return solveRec(n ,1, 0);

        vector<vector<int>> dp(n+2,vector<int>(n , -1));

        return solveMem(n,1,0,dp);
    }
};
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