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
#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)n;i++)
#define rep1(i,n) for(int i=1;i<=(int)n;i++)
typedef long long ll;
using namespace std;
const int mod = 1000000007;
ll modpow(ll a, ll n){
  long long r = 1;
  while (n) {
    r = r * ( (n%2)?a:1 ) %mod;
    a = a * a % mod;
    n >>= 1;
  }
  return r;
}
int main(void){
    ll n;cin>>n;
    vector<ll> a(n);
    rep(i,n) cin>>a[i];
    map<ll,ll> mp2;
    rep(i,n){
        ll x=a[i];
        map<ll,ll> mp1;
        for(int i=2;i*i<=x;i++){
            while(x%i==0){
                x/=i;
                mp1[i]++;
            }
        }
        if(x>1)mp1[x]++;
        for(auto& p:mp1){
            mp2[p.first]=max(mp2[p.first],p.second);
        }
    }
    ll lcm=1;
    for(auto& p : mp2){
        lcm*=modpow(p.first,p.second)%mod;
        lcm%=mod;
    }
    ll res=0;
    rep(i,n){
        res+=(lcm*(modpow(a[i],mod-2)%mod))%mod;
        res%=mod;
    }
    cout<<res<<endl;
}