Given are N positive integers A_1,...,A_N.

Consider positive integers B_1, ..., B_N that satisfy the following condition.

Condition: For any i, j such that 1 \leq i < j \leq N, A_i B_i = A_j B_j holds.

Find the minimum possible value of B_1 + ... + B_N for such B_1,...,B_N.

Since the answer can be enormous, print the sum modulo (10^9 +7).

Constraints

* 1 \leq N \leq 10^4
* 1 \leq A_i \leq 10^6
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 ... A_N


Output

Print the minimum possible value of B_1 + ... + B_N for B_1,...,B_N that satisfy the condition, modulo (10^9 +7).

Examples

Input

3
2 3 4


Output

13


Input

5
12 12 12 12 12


Output

5


Input

3
1000000 999999 999998


Output

996989508
#pragma GCC optimize(2)
#include<bits/stdc++.h>
#define ll long long
#define maxn 1000005
#define inf 1e9
#define pb push_back
#define rep(i,a,b) for(int i=a;i<=b;i++)
using namespace std;

inline int read()
{
	int x=0,w=1; char c=getchar();
	while(c<'0'||c>'9') {if(c=='-') w=-1; c=getchar();}
	while(c<='9'&&c>='0') {x=(x<<1)+(x<<3)+c-'0'; c=getchar();}
	return w==1?x:-x;
}

int n,a[maxn],t,ans,p,X[maxn];
const ll mod=1000000007;

inline ll pw(ll a,ll b)
{
	ll ans=1,base=a;
	while(b)
	{
		if(b&1) ans=(ans*base)%mod;
		base=(base*base)%mod; b>>=1;
	}
	return ans;
}

inline void wk(int x)
{
	for(int i=2;i*i<=x;i++)
	{
		int cnt=0;
		if(x%i==0)
		{
			while(x%i==0) x/=i,cnt++;
			X[i]=max(X[i],cnt);
		}
	}
	if(x) X[x]=max(X[x],1);
}

int main()
{
	n=read(); rep(i,1,n) a[i]=read(),wk(a[i]); t=1;
	rep(i,1,maxn-5) if(X[i]) t=(t*pw(i,X[i]))%mod;
	rep(i,1,n) ans=(ans+t*pw(a[i],mod-2)%mod)%mod; cout<<ans<<endl;
	return 0;
}