Imagine you have a special keyboard with the following keys:

Key 1: (A): Print one 'A' on screen.

Key 2: (Ctrl-A): Select the whole screen.

Key 3: (Ctrl-C): Copy selection to buffer.

Key 4: (Ctrl-V): Print buffer on screen appending it after what has already been printed.

Now, you can only press the keyboard for N times (with the above four keys), find out the maximum numbers of 'A' you can print on screen.

Example 1:

Input: N = 3

Output: 3

Explanation:

We can at most get 3 A's on screen by pressing following key sequence:

A, A, A

Example 2:

Input: N = 7

Output: 9

Explanation:

We can at most get 9 A's on screen by pressing following key sequence:

A, A, A, Ctrl A, Ctrl C, Ctrl V, Ctrl V

Note:

1 <= N <= 50
Answers will be in the range of 32-bit signed integer.

C++:

class Solution {

public:

    int maxA(int N) {

        int res = N;

        for (int i = 1; i < N - 2; ++i) {

            res = max(res, maxA(i) * (N - 1 - i));

        }

        return res;

    }

};

C++:

 class Solution {

public:

    int maxA(int N) {

        vector<int> dp(N + 1, 0);

        for (int i = 0; i <= N; ++i) {

            dp[i] = i;

            for (int j = 1; j < i - 2; ++j) {

                dp[i] = max(dp[i], dp[j] * (i - j - 1));

            }

        }

        return dp[N];

    }

};

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