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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.net.ConnectException;
import java.rmi.dgc.Lease;
import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Deque;
import java.util.HashMap;
import java.util.HashSet;
import java.util.List;
import java.util.Map;
import java.util.NoSuchElementException;
import java.util.Objects;
import java.util.Set;
import java.util.Stack;
import java.util.TreeMap;
import java.util.TreeSet;

import static java.util.Comparator.*;

public class Main {
	public static void main(String[] args) {
		Main main = new Main();
		main.solve();
		main.out.close();
	}

	// ======================================================================
	final int MOD = (int)(1e9) + 7;
	// 素因数分解した結果の、素数と指数の組み合わせをセットするマップ								
	Map<Integer, Integer> wk, map = new HashMap<>();
	Sieve sieve = new Sieve(1000000);
	public void solve() {
		int N = ni();
		int[] A = ni(N);
		if(N == 1) {
			out.println(1);
			return;
		}
		int cnt;								
		for (int i = 0; i < N; i++) {								
			wk = sieve.factor(A[i]);							
			for(int key : wk.keySet()) {							
				cnt = wk.get(key);						
				// 指数はその素数の中の最大値を残す　→　最小公倍数の計算で使う						
				map.merge(key, cnt, (v1, v2) -> { return Math.max(v1, v2); });						
			}							
		}								
		// 最小公倍数の計算								
		long lcm = 1;								
		for(int key : map.keySet()) {
			cnt = map.get(key);							
			for (int i = 0; i < cnt; i++) {							
				lcm = (lcm * key) % MOD;
			}
		}
		long ans = 0;
		for (int i = 0; i < N; i++) {
			// 使い方
			//  A ÷ B の結果を mod 1000000007 で割った余りを求める
			ans = (ans + (lcm * modinv(A[i], MOD)) % MOD) % MOD;
		}
		out.println(ans);
	}
	// a の mod m での逆元を返す
	long modinv(long a, long m) {
		long b = m, u = 1, v = 0, wk;
		while (b > 0) {
			long t = a / b;
			a -= t * b; wk = a; a = b; b = wk;
			u -= t * v; wk = u; u = v; v = wk;
		}
		u %= m; 
		if (u < 0) u += m;
		return u;
	}

    //-----------------------------------												
    // 多くの数を素因数分解する場合に使うクラス												
    //-----------------------------------												
    class Sieve {												
    	int n;											
    	int[] f;					// エラトステネスの篩(ふるい）の変形（割った素数を保存する）						
    	List<Integer> primes = new ArrayList<>();					// 素数の配列						
    												
    	// 初期化　n 以下の数を素数判定する　→　これを作るのは１回だけ											
    	public Sieve(int n) {											
    		this.n = n;										
    		f = new int[n+10];										
    		for (int i = 0; i < f.length; i++) {										
			f[i] = i;					// 初期値として全て素数とする				
		}										
    		f[0] = f[1] = -1;						// ０，１は素数でない				
    		for(int i = 2; i*i <= n; i++) {										
    			if(f[i] != i)		continue;			// 素数でない				
    			primes.add(i);					// 素数を保存				
    			for (int j = i*i; j <= n; j += i) {									
				if(f[j] == j)		f[j] = i;		// 割った素数を保存（最初に割った素数）				
			}									
    		}										
    	}											
    	// 素数判定											
    	boolean isPrime(int x) {											
    		return f[x] == x;										
    	}											
    	// 素因数分解　引数  12 --> 2 * 2 * 3　３つ素数がセットされたリストを返す											
    	List<Integer> factorList(int arg) {											
    		int x = arg;										
    		List<Integer> ans = new ArrayList<>();										
    		while(x != 1) {										
    			ans.add(f[x]);									
    			if(f[x] == 0) {									
    				out.println("zero devide  x = " + x + "  arg = " + arg);								
    				x = 1;								
    			} else {									
    				x /= f[x];								
    			}									
    		}										
    		return ans;										
    	}											
    	// 素因数分解　引数　12 --> 2 * 2 * 3  Map で　(2, 2) (3, 1) を返す											
    	Map<Integer, Integer> factor(int x) {											
    		Map<Integer, Integer> ans = new HashMap<>();										
    		List<Integer> flist = factorList(x);										
    		if(flist.size() == 0)	return ans;									
    		for(int p : flist) {										
    			ans.merge(p, 1, Integer::sum);									
    		}										
    		return ans;										
    	}											
    }												

	// ------------------------------------------
	// ライブラリ
	// ------------------------------------------
	// Print
	private PrintWriter out = new PrintWriter(System.out);

	// Scanner
	private FastScanner scan = new FastScanner();

	int ni() {
		return scan.nextInt();
	}

	int[] ni(int n) {
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = ni();
		}
		return a;
	}

	int[][] ni(int y, int x) {
		int[][] a = new int[y][x];
		for (int i = 0; i < y; i++) {
			for (int j = 0; j < x; j++) {
				a[i][j] = ni();
			}
		}
		return a;
	}

	long nl() {
		return scan.nextLong();
	}

	long[] nl(int n) {
		long[] a = new long[n];
		for (int i = 0; i < n; i++) {
			a[i] = nl();
		}
		return a;
	}

	long[][] nl(int y, int x) {
		long[][] a = new long[y][x];
		for (int i = 0; i < y; i++) {
			for (int j = 0; j < x; j++) {
				a[i][j] = nl();
			}
		}
		return a;
	}

	String ns() {
		return scan.next();
	}

	String[] ns(int n) {
		String[] a = new String[n];
		for (int i = 0; i < n; i++) {
			a[i] = ns();
		}
		return a;
	}

	String[][] ns(int y, int x) {
		String[][] a = new String[y][x];
		for (int i = 0; i < y; i++) {
			for (int j = 0; j < x; j++) {
				a[i][j] = ns();
			}
		}
		return a;
	}
}

class FastScanner {
	private final InputStream in = System.in;
	private final byte[] buffer = new byte[1024];
	private int ptr = 0;
	private int buflen = 0;

	private boolean hasNextByte() {
		if (ptr < buflen) {
			return true;
		} else {
			ptr = 0;
			try {
				buflen = in.read(buffer);
			} catch (IOException e) {
				e.printStackTrace();
			}
			if (buflen <= 0) {
				return false;
			}
		}
		return true;
	}

	private int readByte() {
		if (hasNextByte())
			return buffer[ptr++];
		else
			return -1;
	}

	private static boolean isPrintableChar(int c) {
		return 33 <= c && c <= 126;
	}

	public boolean hasNext() {
		while (hasNextByte() && !isPrintableChar(buffer[ptr]))
			ptr++;
		return hasNextByte();
	}

	public String next() {
		if (!hasNext())
			throw new NoSuchElementException();
		StringBuilder sb = new StringBuilder();
		int b = readByte();
		while (isPrintableChar(b)) {
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}

	public long nextLong() {
		if (!hasNext())
			throw new NoSuchElementException();
		long n = 0;
		boolean minus = false;
		int b = readByte();
		if (b == '-') {
			minus = true;
			b = readByte();
		}
		if (b < '0' || '9' < b) {
			throw new NumberFormatException();
		}
		while (true) {
			if ('0' <= b && b <= '9') {
				n *= 10;
				n += b - '0';
			} else if (b == -1 || !isPrintableChar(b)) {
				return minus ? -n : n;
			} else {
				throw new NumberFormatException();
			}
			b = readByte();
		}
	}

	public int nextInt() {
		long nl = nextLong();
		if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
			throw new NumberFormatException();
		return (int) nl;
	}

	public double nextDouble() {
		return Double.parseDouble(next());
	}
}
