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# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Runtime.InteropServices;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using static Math2;
using static io;
using static Utils;

public class CompetitiveProgramming {
  public void Solve () {
    var N = Int1;
    var A = Ints;
    var L = new Dictionary<int, int> ();
    for (int i = 0; i < N; ++i) {
      var lis = NumberTheory.PrimeFactorization (A[i]);
      foreach (var x in lis) {
        if (!L.ContainsKey ((int) x.Key)) {
          L[(int) x.Key] = x.Value;
        } else L[(int) (x.Key)] = Max (L[(int) x.Key], x.Value);
      }
    }
    long ans = 1;
    foreach (var item in L) {
      ans *= Power (item.Key, item.Value);
      ans %= MOD;
    }
    long answer = 0;
    foreach (var item in A) {
      answer += ans * inv (item);
      answer %= MOD;
    }
    Put (answer);
  }
}

public static class NumberTheory {
  public static Dictionary<long, int> PrimeFactorization (long N) {
    var ret = new Dictionary<long, int> ();
    for (long i = 2; i * i <= N; ++i) {
      int cnt = 0;
      while (N % i == 0) {
        cnt++;
        N /= i;
      }
      if (cnt != 0) ret[i] = cnt;
    }
    if (N >= 2) ret[N] = 1;
    return ret;
  }
  public static Dictionary<int, int> FactoricalPF (int N) {
    var ret = new Dictionary<int, int> ();
    for (int i = 2; i <= N; ++i) {
      int ni = i;
      for (int j = 2; j * j <= ni; ++j) {
        int cnt = 0;
        while (ni % j == 0) {
          ++cnt;
          ni /= j;
        }
        if (cnt == 0) continue;
        if (ret.ContainsKey (j))
          ret[j] += cnt;
        else ret[j] = cnt;
      }
      if (ni >= 2) {
        if (ret.ContainsKey (ni))
          ret[ni] += 1;
        else ret[ni] = 1;
      }
    }
    return ret;
  }
  public static List<long> DivisorEnumrate (long N) {
    var ret = new List<long> ();
    for (long i = 1; i * i <= N; ++i) {
      if (N % i == 0) {
        ret.Add (i);
        ret.Add (N / i);
      }
    }
    return ret;
  }
  public static List<int> seive (int n) {
    var ret = new List<int> ();
    bool[] isPrime = new bool[n + 1];
    for (int i = 1; i <= n; ++i) isPrime[i] = true;
    isPrime[1] = false;
    for (int i = 1; i <= n; ++i) {
      int j = i;
      if (isPrime[i]) ret.Add (i);
      else continue;
      while (j <= n) {
        j += i;
        if (j > n) continue;
        isPrime[j] = false;
      }
    }
    return ret;
  }
  public static bool isPrime (long n) {
    for (int i = 2; i * i <= n; ++i) {
      if (n % i == 0) return false;
    }
    return true;
  }
}

public static class Math2 {
  public const int INF = 1 << 29;
  public const long INFL = 1L << 60;
  public const long MOD = 1000000007;
  public const int MOD2 = 998244353;

  public static long Power (long a, long b, long MOD = 1000000007) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a % MOD;
      a = a * a % MOD;
      b >>= 1;
    }
    return res;
  }
  public static long Power2 (long a, long b) //i^N
  {
    long res = 1;
    while (b > 0) {
      if ((b & 1) != 0) res = res * a;
      a = a * a;
      b >>= 1;
    }
    return res;
  }
  public static long GCD (long a, long b) {
    while (b > 0) {
      var r = a % b;
      a = b;
      b = r;
    }
    return a;
  }
  public static long LCM (long a, long b) => (b / GCD (a, b)) * a;
  public static long Comb (long n, long r, int MOD = 1000000007) {
    if (r > n - r) r = n - r;
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno = (Deno * i) % MOD;
      Nume = Nume * (n - i + 1) % MOD;
    }
    return (Nume * inv (Deno)) % MOD;
  }
  public static long Comb2 (long n, long r) {
    long Nume = 1;
    long Deno = 1;

    if (r > n - r) r = n - r;
    for (long i = 1; i <= r; ++i) {
      Deno *= i;
      Nume *= n - i + 1;
    }
    return Nume / Deno;
  }
  public static long inv (long x, int MOD = 1000000007) {
    return Power (x, MOD - 2, MOD);
  }
}
public static class Utils {
  public static void Swap<T> (ref T A, ref T B) {
    T x = A;
    A = B;
    B = x;
  }
  public static int DigitSum (int N) {
    string s = N.ToString ();
    int ret = 0;
    for (int i = 0; i < s.Length; ++i) ret += s[i] - '0';
    return ret;
  }
  public static string ConvertBase (long N, int K) {
    StringBuilder ret = new StringBuilder ();
    while (N > 0) {
      var r = N % K;
      N /= K;
      ret.Append (r);
    }
    return new string (ret.ToString ().ToCharArray ().Reverse ().ToArray ());
  }
}
class Program {
  static void Main (string[] args) {
    var CompetitiveProgramming = new CompetitiveProgramming ();
    CompetitiveProgramming.Solve ();
  }
}
public static class io {
  public static string Str => Console.ReadLine ();
  public static string[] Strs => Str.Split (' ');
  public static long[] Longs => Strs.Select (long.Parse).ToArray ();
  public static int[] Ints => Strs.Select (int.Parse).ToArray ();
  public static char[] Chars => Str.ToArray ();
  public static double[] Doubles => Strs.Select (double.Parse).ToArray ();
  public static long Long1 => Longs[0];
  public static int Int1 => Ints[0];
  public static char Char1 => Chars[0];
  public static double Double1 => Doubles[0];
  public static long[] VerticalRead (int N) { long[] A = new long[N]; for (int i = 0; i < N; ++i) A[i] = Long1; return A; }
  public static void Put (string a) => Console.WriteLine (a);
  public static void Put (params object[] i) => Put (string.Join (" ", i));
  public static void Put<T> (IEnumerable<T> a) => Put (string.Join (" ", a));
  public static void VerticalPut<T> (IEnumerable<T> a) { foreach (var z in a) Put (z); }
  public static void YN (bool i) {
    if (i) Put ("Yes");
    else Put ("No");
  }
}