（中）Educational Codeforces Round 18 E题Colored Balls（简单的数学）解题报告

E. Colored Balls

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

There are n boxes with colored balls on the table. Colors are numbered from 1 to n. i-th box contains ai balls, all of which have color i. You have to write a program that will divide all balls into sets such that:

• each ball belongs to exactly one of the sets,
• there are no empty sets,
• there is no set containing two (or more) balls of different colors (each set contains only balls of one color),
• there are no two sets such that the difference between their sizes is greater than 1.

Print the minimum possible number of sets.

Input

The first line contains one integer number n (1 ≤ n ≤ 500).

The second line contains n integer numbers a1, a2, ... , an (1 ≤ ai ≤ 109).

Output

Print one integer number — the minimum possible number of sets.

Examples

input

3
4 7 8

output

5

input

2
2 7

output

4

Note

In the first example the balls can be divided into sets like that: one set with 4 balls of the first color, two sets with 3 and 4 balls, respectively, of the second color, and two sets with 4 balls of the third color.

 

这场educational round 真的学到很多……C题代码极易有缺陷，FST了无数人，D、E都非常简单，但C题这一关真的需要细想才能过去……

将数据排序之后依照将最小的那个分成的个数的情况来挨个看。

[个数*(x-1),个数*x]区间内的数都能取得，x为符合“个数*x">=a[1]的最小的x。

（注意如果a[1]%x==0时，令x+1为x对于a[1]也没有问题，所以这时x+1也要判断下）

之后再用这个x对后面的下标2——n的数进行检验。检验方式依旧是看a[i]是否在那个区间里，不过，这时是x固定，求个数。

#include <iostream>
#include <string>
#include <algorithm>
#include <cstring>
#include <cstdio>
#include <cmath>
typedef long long ll;
typedef unsigned long long ull;
using namespace std;
const int MAX=505;
int a[MAX];
int n;
ll an,tem;
int da;
int check(int fen,int shu)
{
    int ge=(shu+fen-1)/fen;
    if(ge*(fen-1)<=shu)
        return ge;
    return 0;
}
ll check2(int da)
{
    ll re=0;
    int tem;
    for(int i=2;i<=n;i++)
    {
        tem=check(da,a[i]);
        if(tem==0)
            return -1;
        else
            re+=tem;
    }
    return re;
}
int main()
{
    scanf("%d",&n);
    for(int i=1;i<=n;i++)
        scanf("%d",&a[i]);
    sort(a+1,a+1+n);
    for(int i=1;i<=sqrt(a[1]);i++)
    {
        da=(a[1]+i-1)/i;
        if(a[1]%da==0)
        {
            da++;
            an=check(da,a[1]);
            tem=check2(da);
            if(tem!=-1)
            {
                an+=tem;
                cout<<an<<"\n";
                return 0;
            }
            da--;
        }
            an=check(da,a[1]);
            tem=check2(da);
            if(tem!=-1)
            {
                an+=tem;
                cout<<an<<"\n";
                return 0;
            }
    }
}

 

E. Colored Balls

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

There are n boxes with colored balls on the table. Colors are numbered from 1 to n. i-th box contains ai balls, all of which have color i. You have to write a program that will divide all balls into sets such that:

• each ball belongs to exactly one of the sets,
• there are no empty sets,
• there is no set containing two (or more) balls of different colors (each set contains only balls of one color),
• there are no two sets such that the difference between their sizes is greater than 1.

Print the minimum possible number of sets.

Input

The first line contains one integer number n (1 ≤ n ≤ 500).

The second line contains n integer numbers a1, a2, ... , an (1 ≤ ai ≤ 109).

Output

Print one integer number — the minimum possible number of sets.

Examples

input

3
4 7 8

output

5

input

2
2 7

output

4

Note

In the first example the balls can be divided into sets like that: one set with 4 balls of the first color, two sets with 3 and 4 balls, respectively, of the second color, and two sets with 4 balls of the third color.