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A. Fox and Number Game

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFox Ciel is playing a game with numbers now.

Ciel has *n* positive integers: *x*_{1}, *x*_{2}, ..., *x*_{n}. She can do the following operation as many times as needed: select two different indexes *i* and *j* such that *x*_{i} > *x*_{j} hold, and then apply assignment *x*_{i} = *x*_{i} - *x*_{j}. The goal is to make the sum of all numbers as small as possible.

Please help Ciel to find this minimal sum.

Input

The first line contains an integer *n* (2 ≤ *n* ≤ 100). Then the second line contains *n* integers: *x*_{1}, *x*_{2}, ..., *x*_{n} (1 ≤ *x*_{i} ≤ 100).

Output

Output a single integer — the required minimal sum.

Examples

Input

2

1 2

Output

2

Input

3

2 4 6

Output

6

Input

2

12 18

Output

12

Input

5

45 12 27 30 18

Output

15

Note

In the first example the optimal way is to do the assignment: *x*_{2} = *x*_{2} - *x*_{1}.

In the second example the optimal sequence of operations is: *x*_{3} = *x*_{3} - *x*_{2}, *x*_{2} = *x*_{2} - *x*_{1}.

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

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