Where is the Ghost

The ghost exploration team find some 1D coordinate where the cursed object is located. You will be given $N$ such cursed positions. All the locations are integers. You need to find the possible ghost spawning area using those cursed object positions.

The ghost has a special affection for numbers $1$ to $9$. An area is said to be a ghost spawning area if it is divisible by all the numbers from $1$ to $9$.

Being a member of the ghost exploration team, you need to find out the number of ways of selecting one or more cursed object locations from those $N$ locations such that the product of those locations returns a ghost spawning area.

Since the answer can be very big, output the answer modulo $10^9 + 7$.

Input

The first line of input is an integer $N$. The next line will contain $N$ different integer numbers.

Constraints

• $1 \leq N \leq 10^4$

• $1\leq\text{all cursed positions}\leq 10^4$

Output

Print the number of ways of selecting one or more cursed object locations modulo $10^9 + 7$ such that the product of those locations becomes a ghost spawning area.

Samples

Input	Output
7 1 2 3 4 5 6 7	4

Input	Output
6 1 2 3 4 5 6	0