Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

3
2 3 4

Sample Output 1

13

Let B_1=6, B_2=4, and B_3=3, and the condition will be satisfied.

Sample Input 2

5
12 12 12 12 12

Sample Output 2

5

We can let all B_i be 1.

Sample Input 3

3
1000000 999999 999998

Sample Output 3

996989508

Print the sum modulo (10^9+7).

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#pragma GCC optimize("O2")
#pragma GCC optimize("O3")
#pragma GCC target("avx")
#define rep(i,N) for(int i=0;i<(int)N;i++)
const int MOD=1e9+7,MAX=1e6;
static inline int IN(void)
{
  int x=0,f=0,c=getchar();while(c<48||c>57){f^=c==45,c=getchar();}
  while(c>47&&c<58){x=x*10+c-48,c=getchar();}return f?-x:x;
}
typedef struct{int SPF[1000001];int Primes[1000001];int count[1000001];int sz;}Template;
struct T{int fact[1000001],inv[1000001];};
Template P;struct T MODINV;
static inline int MPow(int a,int b){return b?1l*MPow(1l*a*a%MOD,b>>1)*(b&1?a:1)%MOD:1;}
static inline void ready(void)
{
  *P.SPF=1,*P.Primes=2,*P.count=0,P.sz=1;
  rep(i,MAX/2)P.SPF[2*(i+1)]=2,P.SPF[2*(i+1)-1]=2*(i+1)-1;
  rep(i,MAX/2-1)
  {
    int x=2*(i+1)+1;if(P.SPF[x]==x)P.Primes[P.sz++]=x;
    rep(j,P.sz)
    {
      if(P.Primes[j]<=P.SPF[x]&&x*P.Primes[j]<=MAX)P.SPF[x*P.Primes[j]]=P.Primes[j];
      else break;
    }
  }
  rep(i,P.sz/2)P.count[P.Primes[2*i]]=P.count[P.Primes[2*i+1]]=0;
}
static inline void init(void)
{
  MODINV.fact[0]=1;rep(i,MAX)MODINV.fact[i+1]=1l*MODINV.fact[i]*(i+1)%MOD;
  MODINV.inv[MAX]=MPow(MODINV.fact[MAX],MOD-2);
  rep(i,MAX)MODINV.inv[MAX-1-i]=1l*MODINV.inv[MAX-i]*(MAX-i)%MOD;
}
int main(void)
{
  int N=IN(),A=0,invsum=0,k=0,lcm=1,x=0,temp[10000],box[168]={};ready();init();
  rep(i,N)
  {
    A=IN();invsum=(invsum+1l*MODINV.fact[A-1]*MODINV.inv[A]%MOD)%MOD;
    rep(j,168){x=0;while(A%P.Primes[j]==0){A/=P.Primes[j];if(box[j]<++x)box[j]=x;}}
    if(A!=1){temp[k++]=A;}
  }
  rep(i,168){rep(j,box[i]){lcm=1l*lcm*P.Primes[i]%MOD;}}
  x=-1;rep(i,k){if(x!=temp[i]){lcm=1l*lcm*temp[i]%MOD;x=temp[i];}}
  x=1l*lcm*invsum%MOD;return printf("%d\n",x),0;
}