Flatten

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 ... A_N

outputFormat

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

样例

3
2 3 4

13