Description

Xiao Y has a password lock with five dials. As shown in the figure, there are numbers from $0$ to $9$ on each dial. Each dial is a loop from $0$ to $9$, where $9$ can change to $0$ or $8$ by shifting one position.

Because it is relatively safe on campus, the locking method adopted by Xiao Y is: starting from the correct password, randomly turning the password lock only once; Each time, only one dial is rotated by a certain amplitude or two adjacent dials are rotated simultaneously.

When Little Y chooses to rotate two adjacent dials at the same time, the amplitude of rotation of the two dials is the same, that is, Little Y can convert the password lock from $\tt{0\;0\;1\;1\;5}$ to $\tt{1\;1\;1\;1\;5}$, but not to $\tt{1\;2\;1\;1\;5}$.

After a long time, Xiao Y was also worried about the safety of locking the car like this, so he recorded the $n$ states of the password lock after locking the car. Note that none of these $n$ states are the correct password.

How many possible correct passwords does Xiao Y have to verify the security of locking the car in this way, so that each correct password can generate all n states of the password lock after locking the car according to the locking method he uses.

Input

The first line of input contains a positive integer $n$, representing the number of states of the password lock after the car is locked.

The next $n$ line contains five integers per line, representing the state of a password lock.

Output

Output a line containing an integer representing how many correct passwords the $n$ states of the password lock can correspond to according to the given locking method.

Samples

1
0 0 1 1 5

81

Tips

[Sample Input 1 Explanation]

There are a total of $81$ possible solutions. There are $45$ options for rotating one dial and $36$ options for rotating two dials.

[Sample 2]

See lock/lock2.in and lock/lock2.ans in the player directory.

[Data Range]

For all test data: $1 \leq n \leq 8$.

Special property A: Ensure that all correct passwords can obtain the $n$ states given by the test data by rotating only one dial.