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.Generic;
using System.Text;
using CompLib.Collections;
using CompLib.Mathematics;
using CompLib.Util;

public class Program
{
    private int N;
    private int[] A;

    public void Solve()
    {
        var sc = new Scanner();
        N = sc.NextInt();
        A = sc.IntArray();
        
        var map = new HashMap<int,int>();

        foreach (int t in A)
        {
            int tmp = t;
            for (int i = 2; i * i <= tmp; i++)
            {
                if (tmp % i == 0)
                {
                    int cnt = 0;
                    while (tmp%i == 0)
                    {
                        cnt++;
                        tmp /= i;
                    }

                    map[i] = Math.Max(map[i], cnt);
                }
            }

            if (tmp != 1)
            {
                map[tmp] = Math.Max(map[tmp], 1);
            }
        }

        ModInt lcm = 1;
        foreach (KeyValuePair<int,int> pair in map)
        {
            lcm *= ModInt.Pow(pair.Key,pair.Value);
        }

        ModInt ans = 0;
        foreach (int i in A)
        {
            ans += lcm * ModInt.Inverse(i);
        }

        Console.WriteLine(ans);
    }

    public static void Main(string[] args) => new Program().Solve();
}

namespace CompLib.Collections
{
    using System.Collections.Generic;

    public class HashMap<TKey, TValue> : Dictionary<TKey, TValue>
    {
        public new TValue this[TKey key]
        {
            get
            {
                TValue o;
                return TryGetValue(key, out o) ? o : default(TValue);
            }
            set { base[key] = value; }
        }
    }
}

// https://bitbucket.org/camypaper/complib
namespace CompLib.Mathematics
{
    #region ModInt

    /// <summary>
    /// [0,<see cref="Mod"/>) までの値を取るような数
    /// </summary>
    public struct ModInt
    {
        /// <summary>
        /// 剰余を取る値．
        /// </summary>
        public const long Mod = (int) 1e9 + 7;

        /// <summary>
        /// 実際の数値．
        /// </summary>
        public long num;

        /// <summary>
        /// 値が <paramref name="n"/> であるようなインスタンスを構築します．
        /// </summary>
        /// <param name="n">インスタンスが持つ値</param>
        /// <remarks>パフォーマンスの問題上，コンストラクタ内では剰余を取りません．そのため，<paramref name="n"/> ∈ [0,<see cref="Mod"/>) を満たすような <paramref name="n"/> を渡してください．このコンストラクタは O(1) で実行されます．</remarks>
        public ModInt(long n)
        {
            num = n;
        }

        /// <summary>
        /// このインスタンスの数値を文字列に変換します．
        /// </summary>
        /// <returns>[0,<see cref="Mod"/>) の範囲内の整数を 10 進表記したもの．</returns>
        public override string ToString()
        {
            return num.ToString();
        }

        public static ModInt operator +(ModInt l, ModInt r)
        {
            l.num += r.num;
            if (l.num >= Mod) l.num -= Mod;
            return l;
        }

        public static ModInt operator -(ModInt l, ModInt r)
        {
            l.num -= r.num;
            if (l.num < 0) l.num += Mod;
            return l;
        }

        public static ModInt operator *(ModInt l, ModInt r)
        {
            return new ModInt(l.num * r.num % Mod);
        }

        public static implicit operator ModInt(long n)
        {
            n %= Mod;
            if (n < 0) n += Mod;
            return new ModInt(n);
        }

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Pow(ModInt v, long k)
        {
            return Pow(v.num, k);
        }

        /// <summary>
        /// 与えられた 2 つの数値からべき剰余を計算します．
        /// </summary>
        /// <param name="v">べき乗の底</param>
        /// <param name="k">べき指数</param>
        /// <returns>繰り返し二乗法により O(N log N) で実行されます．</returns>
        public static ModInt Pow(long v, long k)
        {
            long ret = 1;
            for (k %= Mod - 1; k > 0; k >>= 1, v = v * v % Mod)
                if ((k & 1) == 1)
                    ret = ret * v % Mod;
            return new ModInt(ret);
        }

        /// <summary>
        /// 与えられた数の逆元を計算します．
        /// </summary>
        /// <param name="v">逆元を取る対象となる数</param>
        /// <returns>逆元となるような値</returns>
        /// <remarks>法が素数であることを仮定して，フェルマーの小定理に従って逆元を O(log N) で計算します．</remarks>
        public static ModInt Inverse(ModInt v)
        {
            return Pow(v, Mod - 2);
        }
    }

    #endregion

    #region Binomial Coefficient

    public class BinomialCoefficient
    {
        public ModInt[] fact, ifact;

        public BinomialCoefficient(int n)
        {
            fact = new ModInt[n + 1];
            ifact = new ModInt[n + 1];
            fact[0] = 1;
            for (int i = 1; i <= n; i++)
                fact[i] = fact[i - 1] * i;
            ifact[n] = ModInt.Inverse(fact[n]);
            for (int i = n - 1; i >= 0; i--)
                ifact[i] = ifact[i + 1] * (i + 1);
            ifact[0] = ifact[1];
        }

        public ModInt this[int n, int r]
        {
            get
            {
                if (n < 0 || n >= fact.Length || r < 0 || r > n) return 0;
                return fact[n] * ifact[n - r] * ifact[r];
            }
        }

        public ModInt RepeatedCombination(int n, int k)
        {
            if (k == 0) return 1;
            return this[n + k - 1, k];
        }
    }

    #endregion
}


namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(Separator);
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}