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
import java.util.*; import java.io.*; import java.math.*;
public class Main{
	//Don't have to see. start------------------------------------------
	static class InputIterator{
		ArrayList<String> inputLine = new ArrayList<String>(1024);
		int index = 0; int max; String read;
		InputIterator(){
			BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
			try{
				while((read = br.readLine()) != null){
					inputLine.add(read);
				}
			}catch(IOException e){}
			max = inputLine.size();
		}
		boolean hasNext(){return (index < max);}
		String next(){
			if(hasNext()){
				return inputLine.get(index++);
			}else{
				throw new IndexOutOfBoundsException("There is no more input");
			}
		}
	}
	static HashMap<Integer, String> CONVSTR = new HashMap<Integer, String>();
	static InputIterator ii = new InputIterator();//This class cannot be used in reactive problem.
	static PrintWriter out = new PrintWriter(System.out);
	static void flush(){out.flush();}
	static void myout(Object t){out.println(t);}
	static void myerr(Object t){System.err.print("debug:");System.err.println(t);}
	static String next(){return ii.next();}
	static boolean hasNext(){return ii.hasNext();}
	static int nextInt(){return Integer.parseInt(next());}
	static long nextLong(){return Long.parseLong(next());}
	static double nextDouble(){return Double.parseDouble(next());}
	static ArrayList<String> nextStrArray(){return myconv(next(), 8);}
	static ArrayList<String> nextCharArray(){return myconv(next(), 0);}
	static ArrayList<Integer> nextIntArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Integer> ret = new ArrayList<Integer>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Integer.parseInt(input.get(i)));
		}
		return ret;
	}
	static ArrayList<Long> nextLongArray(){
		ArrayList<String> input = nextStrArray(); ArrayList<Long> ret = new ArrayList<Long>(input.size());
		for(int i = 0; i < input.size(); i++){
			ret.add(Long.parseLong(input.get(i)));
		}
		return ret;
	}
	static String myconv(Object list, int no){//only join
		String joinString = CONVSTR.get(no);
		if(list instanceof String[]){
			return String.join(joinString, (String[])list);
		}else if(list instanceof ArrayList){
			return String.join(joinString, (ArrayList)list);
		}else{
			throw new ClassCastException("Don't join");
		}
	}
	static ArrayList<String> myconv(String str, int no){//only split
		String splitString = CONVSTR.get(no);
		return new ArrayList<String>(Arrays.asList(str.split(splitString)));
	}
	public static void main(String[] args){
		CONVSTR.put(8, " "); CONVSTR.put(9, "\n"); CONVSTR.put(0, "");
		
		solve();flush();
		
	}
	//Don't have to see. end------------------------------------------
	static void solve(){//Here is the main function
		
		int N = nextInt();
		ArrayList<Long> list = nextLongArray();
		final int mod = 1000000007;
		HashMap<Long, Integer> lcmFact = new HashMap<Long, Integer>();
		for(int i = 0; i < N; i++){
			if(isPrime(list.get(i))){
				if(!lcmFact.containsKey(list.get(i))){
					lcmFact.put(list.get(i), 1);
				}
				continue;
			}
			HashMap<Long, Integer> aFact = getPrimeFactorization(list.get(i));
			Iterator it = aFact.keySet().iterator();
			while(it.hasNext()){
				long key = (long)it.next();
				if(lcmFact.containsKey(key)){
					lcmFact.put(key, Math.max(lcmFact.get(key), aFact.get(key)));
				}else{
					lcmFact.put(key, aFact.get(key));
				}
			}
		}
		
		long first = 1;
		Iterator it = lcmFact.keySet().iterator();
		while(it.hasNext()){
			long key = (long)it.next();
			first *= originPow(key, lcmFact.get(key), mod);
			first %= mod;
		}
		long output = 0;
		for(int i = 0; i < N; i++){
			output += first * originPow(list.get(i), mod - 2, mod);
			output %= mod;
		}
		myout(output);
		
	}
	//Method addition frame start

static boolean isPrime(long val){
        if(val <= 1 || (val != 2 && val % 2 == 0)){
                return false;
        }else if(val == 2){
                return true;
        }
        double root = Math.floor(Math.sqrt(val));
        for(long i = 3; i <= root; i += 2){
                if(val % i == 0){
                        return false;
                }
        }
        return true;
}

static HashMap<Long,Integer> getPrimeFactorization(Long val){
  HashMap<Long,Integer> primeList = new HashMap<Long,Integer>();
  long div = 2;
  while(val != 1){
    if(val % div == 0){
      int count = 2;
      while(val % (long)Math.pow(div, count) == 0){
        count++;
      }
      if(!primeList.containsKey(div)){
        primeList.put(div, count - 1);
      }else{
        primeList.put(div, primeList.get(div) + (count - 1));
      }
      val /= (long)Math.pow(div, count - 1);
      if(isPrime(val)){
        if(!primeList.containsKey(val)){
          primeList.put(val,1);
        }else{
          primeList.put(val,primeList.get(val) + 1);
        }
        break;
      }
    }else{
      div = (div == 2) ? div + 1 : div + 2;
    }
  }
  return primeList;
}

static long originPow(long x, long n) {return originPow(x,n,-1);}
static long originPow(long x, long n, long m) {
        long ans = 1;
        while (n > 0) {
                if ((n & 1) == 1){
                  ans = ans * x;
                  if(m != -1){ans %= m;}
                }
                x = x * x;
                if(m != -1){x %= m;}
                n >>= 1;
        }
        return ans;
}


	//Method addition frame end
}
