链接：https://codeforces.com/contest/1216/problem/D

There were nn types of swords in the theater basement which had been used during the plays. Moreover there were exactly xx swords of each type. yy people have broken into the theater basement and each of them has taken exactly zz swords of some single type. Note that different people might have taken different types of swords. Note that the values x,yx,y and zz are unknown for you.

The next morning the director of the theater discovers the loss. He counts all swords — exactly aiai swords of the ii-th type are left untouched.

The director has no clue about the initial number of swords of each type in the basement, the number of people who have broken into the basement and how many swords each of them have taken.

For example, if n=3n=3, a=[3,12,6]a=[3,12,6] then one of the possible situations is x=12x=12, y=5y=5 and z=3z=3. Then the first three people took swords of the first type and the other two people took swords of the third type. Note that you don't know values x,yx,y and zz beforehand but know values of nn and aa.

Thus he seeks for your help. Determine the minimum number of people yy, which could have broken into the theater basement, and the number of swords zz each of them has taken.

Input

The first line of the input contains one integer nn (2≤n≤2⋅105)(2≤n≤2⋅105) — the number of types of swords.

The second line of the input contains the sequence a1,a2,…,ana1,a2,…,an (0≤ai≤109)(0≤ai≤109), where aiai equals to the number of swords of the ii-th type, which have remained in the basement after the theft. It is guaranteed that there exists at least one such pair of indices (j,k)(j,k) that aj≠akaj≠ak.

Output

Print two integers yy and zz — the minimum number of people which could have broken into the basement and the number of swords each of them has taken.

Examples

input

Copy

3
3 12 6

output

Copy

5 3

input

Copy

2
2 9

output

Copy

1 7

input

Copy

7
2 1000000000 4 6 8 4 2

output

Copy

2999999987 2

input

Copy

6
13 52 0 13 26 52

output

Copy

12 13

Note

In the first example the minimum value of yy equals to 55, i.e. the minimum number of people who could have broken into the basement, is 55. Each of them has taken 33 swords: three of them have taken 33 swords of the first type, and two others have taken 33 swords of the third type.

In the second example the minimum value of yy is 11, i.e. the minimum number of people who could have broken into the basement, equals to 11. He has taken 77 swords of the first type.

题解：

这题总结起来就是求多个数的最小公约数，这里有一个性质，a,b,c三个数如果a和b的最小公约数是x，x和c的最小公约数是y那么y是所有数的最小公约数

代码：

#include<bits/stdc++.h>
using namespace std;
long long a[1000001],max1=0,b[1000001];
int main()
{
	long long n,s=0,max2;
	cin>>n;
	for(int i=1;i<=n;i++)
	{
		cin>>a[i];
		max1=max(max1,a[i]);
	}
	for(int i=1;i<=n;i++)
	{
		b[i]=max1-a[i];
		s+=b[i];
	}
	max2=b[1];
	for(int i=1;i<=n;i++)
	{
		if(b[i]==0)
		continue;
		max2=__gcd(b[i],max2);
	}
	cout<<s/max2<<" "<<max2<<endl;
}