Problem Description

Yamunaku-kun came up with a game using a piece of paper and an integer sequence of length $N$, $A_1, A_2, \ldots, A_N$.

First, write any positive integer on the paper. Then perform $N$ operations. In the $i$-th operation $(1 \le i \le N)$, do one of the following:

• Let $X$ be the number currently written on the paper. Compute $Y = \left\lfloor \frac{A_i}{X} \right\rfloor$ (where $\lfloor x \rfloor$ denotes the integer part of $x$). Replace the number on the paper with $Y$ and gain $Y$ points. Note that this operation cannot be performed if $X > A_i$.
• Do nothing. No points are gained.

Yamunaku-kun wants to maximize the total score obtained from $N$ operations.

Find the maximum score Yamunaku-kun can achieve by optimally choosing the initial number on the paper and performing the $N$ operations.

Input Format

The input is given from the standard input in the following format:

$N$ $A_1$ $A_2$ $\ldots$ $A_N$

Output Format

Output the maximum score Yamunaku-kun can achieve in one line.

Sample Input and Output

Sample Input #1

3
3 6 9

Sample Output #1

10

Sample Input #2

3
10 3 4

Sample Output #2

10

Sample Input #3

1
1000

Sample Output #3

1000

Sample Input #4

10
87 72 55 81 12 59 1 10 18 53

Sample Output #4

166

Notes/Hints

Constraints

• $1 \le N \le 1000$
• $1 \le A_i \le 10^6$
• All inputs are integers.

Partial Points

This problem has partial points.

• Correctly solving the problem for inputs where $A_i \le 1000$ for all $i (1 \le i \le N)$ will award $300$ points.

Sample Explanation 1

• First, write $2$ on the paper.
• In the 1st operation, replace the number on the paper with $\left\lfloor \frac{3}{2} \right\rfloor = 1$ and gain $1$ point.
• In the 2nd operation, do nothing.
• In the 3rd operation, replace the number on the paper with $\left\lfloor \frac{9}{1} \right\rfloor = 9$ and gain $9$ points.
  The total score is $10$, which is the maximum. Note that there are other ways to achieve $10$ points.

见题面 Input 部分

见题面 Output 部分