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 Julia (0.5.0) (judge verdict: Accepted)

function main()
	mod=10^9+7
	N=parse(Int,readline())
	A=map(x->parse(Int,x),split(readline()))
	ans=0
	for a=A
		ans+=invmod(a,mod)
		ans%=mod
	end
	for i=2:10^3
		c=0
		for j=1:N
			n=0
			while A[j]%i==0
				A[j]=div(A[j],i)
				n+=1
			end
			if c<n
				c=n
			end
		end
		ans=ans*i^c%mod
	end
	sort!(A)
	i=1
	while i<=N&&A[i]==1
		i+=1
	end
	while i<=N
		while i<N&&A[i]==A[i+1]
			i+=1
		end
		ans=ans*A[i]%mod
		i+=1
	end
	println(ans)
end
main()