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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.InputMismatchException;
import java.util.Map;
import java.util.TreeMap;
import java.util.Vector;
public class Main implements Runnable{
	               	                    static final long MAX = 464897L;
	                    static class InputReader
	                    {
	                        private InputStream stream;
	                        private byte[] buf = new byte[1024];
	                        private int curChar;
	                        private int numChars;
	                        private SpaceCharFilter filter;
	                        private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	                 
	                        public InputReader(InputStream stream)
	                        {
	                            this.stream = stream;
	                        }
	                        
	                        public int read()
	                        {
	                            if (numChars==-1) 
	                                throw new InputMismatchException();
	                            
	                            if (curChar >= numChars)
	                            {
	                                curChar = 0;
	                                try 
	                                {
	                                    numChars = stream.read(buf);
	                                }
	                                catch (IOException e)
	                                {
	                                    throw new InputMismatchException();
	                                }
	                                
	                                if(numChars <= 0)                
	                                    return -1;
	                            }
	                            return buf[curChar++];
	                        }
	                     
	                        public String nextLine()
	                        {
	                            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        public int nextInt()
        {
            int c = read();
            
            while(isSpaceChar(c)) 
                c = read();
            
            int sgn = 1;
            
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            
            int res = 0;
            do 
            {
                if(c<'0'||c>'9') 
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c)); 
            
            return res * sgn;
        }
        
        public long nextLong() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            
            do 
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            while (!isSpaceChar(c));
                return res * sgn;
        }
        
        public double nextDouble() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') 
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') 
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') 
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) 
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
        
        public String readString() 
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do 
            {
                res.appendCodePoint(c);
                c = read();
            } 
            while (!isSpaceChar(c));
            
            return res.toString();
        }
     
        public boolean isSpaceChar(int c) 
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
     
        public String next() 
        {
            return readString();
        }
        
        public interface SpaceCharFilter 
        {
            public boolean isSpaceChar(int ch);
        }
    }
     
    public static void main(String args[]) throws Exception
    {
        new Thread(null, new Main(),"Main",1<<26).start();
    }   
    static long gcd(long a, long b) 
    { 
      if (b == 0) 
        return a; 
      return gcd(b, a % b);  
    } 
    static long lcm(long a,long b) {
        return (a*b)/gcd(a,b);
    }
    int maxn = 1000005;
    long MOD = 1000000007;
    long prime = 29;
    ArrayList<Integer> adj[];
    static class Node implements Comparable<Node>{
		int destination;
		long weight;
		Node(int destination,long weight){
			this.destination = destination;
			this.weight = weight;
		}
		Node(){
			
		}
		@Override
		public int compareTo(Node n) {
			return Long.signum(weight - n.weight);
		}
	}
    int[] val;
    boolean[] visited;
    int length(int n) {
    	int count = 0;
    	while(n != 0) {
    		n = n/10;
    		count++;
    	}
    	return count;
    }
	public void run() 
    {
        InputReader sc = new InputReader(System.in);
        PrintWriter w = new PrintWriter(System.out);
        int n = sc.nextInt();
        sieve();
        max = new TreeMap();
        int[] arr = new int[n];
        long lcm = 1;
        for(int i = 0;i < n;i++) {
        	arr[i] = sc.nextInt();
        	getFactorization(arr[i]);
        }
        long ans = 1;
        for(Integer key: max.keySet()) {
        	long tans = power(key,max.get(key),MOD);
        	ans = (ans * tans) % MOD;
        }
        long fans = 0;
        for(int i = 0;i < n;i++) {
        	long curr = (ans * power(arr[i],MOD-2,MOD)) % MOD;
        	fans = (fans + curr) % MOD;
        }
        w.println(fans);
        w.close();
    } 
	static final int MAXN = 1000001; 
    
    // stores smallest prime factor for every number 
    static int spf[] = new int[MAXN]; 
       
    // Calculating SPF (Smallest Prime Factor) for every 
    // number till MAXN. 
    // Time Complexity : O(nloglogn) 
    static void sieve() 
    { 
        spf[1] = 1; 
        for (int i=2; i<MAXN; i++) 
       
            // marking smallest prime factor for every 
            // number to be itself. 
            spf[i] = i; 
       
        // separately marking spf for every even 
        // number as 2 
        for (int i=4; i<MAXN; i+=2) 
            spf[i] = 2; 
       
        for (int i=3; i*i<MAXN; i++) 
        { 
            // checking if i is prime 
            if (spf[i] == i) 
            { 
                // marking SPF for all numbers divisible by i 
                for (int j=i*i; j<MAXN; j+=i) 
       
                    // marking spf[j] if it is not  
                    // previously marked 
                    if (spf[j]==j) 
                        spf[j] = i; 
            } 
        } 
    } 
       
    static TreeMap<Integer,Integer> max ;
    static void getFactorization(int x) 
    { 
        Map<Integer,Integer> tmap = new TreeMap();
        while (x != 1) 
        { 
        	if(!tmap.containsKey(spf[x])) {
        		tmap.put(spf[x],0);
        	}
            tmap.put(spf[x],tmap.get(spf[x]) + 1); 
            x = x / spf[x]; 
        } 
        for(Integer key: tmap.keySet()) {
        	if(max.containsKey(key)) {
        		max.put(key,Math.max(max.get(key), tmap.get(key)));
        	}else {
        		max.put(key, tmap.get(key));
        	}
        }
    } 
	public int[] findCell(int n,long ind) { 
		ind++;
        long ans = 0;
        long first = 0;
        long second = 3*n;
        long third = n;
        long four = 2*n;
        long rem = -1;
        long newNum = 0;
        for(long sum = 0;sum <= 3*n-3;sum++){
            long tans = (sum + 2) * (sum + 1) /2;
            if(second <= sum){
             	tans = tans - ((sum - second + 2) * (sum - second + 1))/2;   
            }
            if(third <= sum) {
             	tans = tans - 3 * ((sum - third + 2) * (sum - third + 1))/2;   
            }
            if(four <= sum) {
                tans = tans + 3 * ((sum - four + 2) * (sum - four + 1))/2; 
            }
            if(ans + tans >= ind){
                rem = sum;
                newNum = ind - ans;
                break;
            }else{
             	ans += tans;   
            }
        }
        System.out.println(rem + " " + newNum);
        int[] three = new int[3];
        long cans = 0;
        for(long val = 0;val < n;val++){
            long possible = 0;
            possible = rem - val + 1;
            if(rem - val >= n) {
            	possible = possible - 2*(rem - val - n + 1);
            }
            if(rem - val > 2*n - 2) {
            	possible = 0;
            }
            if(cans + possible >= newNum) {
                three[0] = (int)val;
                rem = rem - val;
                newNum = newNum - cans;
                break;
            }else{
             	cans += possible;   
            }
        }
        System.out.println(rem + " " + newNum);
        for(long val = 0;val < n;val++){
         	if(rem - val >= 0 && rem - val < n){
             	newNum--;
                if(newNum == 0){
                 	three[1] = (int)val;
                    three[2] = (int)(rem - val);
                }
            }
        }
        return three;
    }
	    
	static long power(long a,long b,long MOD) {
        long ans = 1;
        a = a % MOD;
        while(b != 0) {
            if(b % 2 == 1) {
                ans = (ans * a) % MOD;
            }
            a = (a * a) % MOD;
            b = b/2;
        }
        return ans;
    }
    class Equal implements Comparable<Equal>{
    	Character a;
    	int b;
    	public Equal(char a,int b){
    		this.a = a;
    		this.b = b;
    	}
		@Override
		public int compareTo(Equal an) {
			// TODO Auto-generated method stub
			return this.a.compareTo(an.a);
		}
    }
    class Pair implements Comparable<Pair>{
        long a;
        long b;
        long c;
        Pair(long a,long b,long c){
            this.b = b;
            this.a = a;
            this.c = c;
        }
        public boolean equals(Object o) {
            Pair p = (Pair)o;
            return this.a == p.a && this.b == p.b && this.c == p.c;
        }
        public int hashCode(){
            return Long.hashCode(a)*27 + Long.hashCode(b)*31;
        }
        public int compareTo(Pair p) {
       	     return Long.compare(this.a,p.a);
        }
    }
    
    class Pair3 implements Comparable<Pair3>{
        int a;
        int b;
        int c;
        Pair3(int a,int b,int c){
            this.b = b;
            this.a = a;
            this.c = c;
        }
        public boolean equals(Object o) {
            Pair3 p = (Pair3)o;
            return this.a == p.a && this.b == p.b && this.c == p.c;
        }
        public int hashCode(){
            return Long.hashCode(a)*27 + Long.hashCode(b)*31;
        }
        public int compareTo(Pair3 p) {
            return Long.compare(this.b,p.b);
        }
    }
    class Pair2 implements Comparable<Pair2>{
        int a;
        int b;
        int c;
        Pair2(int a,int b,int c){
            this.b = b;
            this.a = a;
            this.c = c;
        }
        public boolean equals(Object o) {
            Pair2 p = (Pair2)o;
            return this.a == p.a && this.b == p.b && this.c == p.c;
        }
        public int hashCode(){
            return Long.hashCode(a)*27 + Long.hashCode(b)*31 + Long.hashCode(c)*3;
        }
        public int compareTo(Pair2 p) {
            return Long.compare(p.a,this.a);
        }
    }
}
