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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.*;
import java.lang.reflect.Array;
import java.util.*;

public class Main {

    // a^n mod
    public static long modPow(long a, long n, long mod) {
        long res = 1;
        while (n > 0) {
            if ((n & 1) != 0)
                res = res * a % mod;
            a = a * a % mod;
            n >>= 1;
        }
        return res;
    }

    // a^{-1} mod
    public static long modInv(long a, long mod) {
        return modPow(a, mod - 2, mod);
    }

    public static boolean isPrime(long n) {
        double root = Math.pow(n, 0.5);
        for(int i=2; i< root+1; i++) {
            if(n%i == 0) {
                return false;
            }
        } 
        return true;
    }

    public static void main(String[] args) {
        FastScanner fs = new FastScanner();
        int n = fs.nextInt();
        int a[] = new int[n];
        for (int i = 0; i < n; i++) {
            a[i] = fs.nextInt();
        }
        long mod = 1000000007;
        int d = 1000001 + 1;
        int lcm_li[] = new int[d];
        Set<Integer> lcm_ex = new HashSet<Integer>();
        int li[] = new int[d];

        for (int i = 0; i < n; i++) {
            
            int t = a[i];
            int tmp[] = new int[t + 1];
            Set<Integer> tmp_ex = new HashSet<>();

            if (isPrime(t)) {
                tmp[t] += 1;
                tmp_ex.add(t);
            } else {

                double root_n = Math.pow(t, 0.5) + 1;

                for (int j = 2; j < root_n; j++) {
                    while (t % j == 0) {
                        tmp[j] += 1;
                        t = t / j;
                        tmp_ex.add(j);
                    }
                }
            }


            for (int j : tmp_ex) {
                if (lcm_li[j] < tmp[j]) {
                    lcm_li[j] = tmp[j];
                    lcm_ex.add(j);
                }
            }
           

        }

        long lcm = 1;
        for (int i : lcm_ex) {
            for (int j = 0; j < lcm_li[i]; j++) {
                lcm *= i;
                lcm %= mod;
            }

        }

        long ans = 0;

        for (int i = 0; i < n; i++) {
            ans += (lcm * modInv(a[i], mod))%mod;
            ans %= mod; 
        }

        System.out.println(ans);
    }
}

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());
    }
}