codeforces Fox and Number Game

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本文介绍了一种算法，用于通过减小特定序列中元素之间的差异来最小化序列的总和。通过选择适当的元素对进行减法操作，最终实现序列和的最小化。

Description

Fox Ciel is playing a game with numbers now.

Ciel has n positive integers: x1, x2, …, xn. She can do the following operation as many times as needed: select two different indexes i and j such that xi > xj hold, and then apply assignment xi = xi - xj. 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: x1, x2, …, xn (1 ≤ xi ≤ 100).

Output

Output a single integer — the required minimal sum.

Sample Input

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

Hint

In the first example the optimal way is to do the assignment: x2 = x2 - x1.

In the second example the optimal sequence of operations is: x3 = x3 - x2, x2 = x2 - x1.

题意：给出一个序列X,能进行如下操作,选择两个下i, j(i != j), 将Xi的值减去Xj, 求怎么样操作能使的最后序列和最小.；

直接求公约数就行；

#include <iostream>
#include <cstring>
#include <algorithm>
using namespace std;

int gcd(int a, int b)
{
    if (b==0) return a;
    return gcd(b,a%b);
}
int main()
{
    int n,x;
    cin>>n;
    cin>>x;
    int g=x;
    for(int i=0; i<n-1; i++)
    {
        cin>>x;
        g=gcd(g, x);
    }
    cout<<g*n<<endl;
    return 0;
}