Five-Dial Lock Security

Little Y uses a five‐dial combination lock to secure his bicycle. Each dial is labeled with the digits from $0$ to $9$ in a cyclic order (i.e. after $9$ comes $0$, and before $0$ comes $9$). When locking his bicycle, starting from the correct password, he performs a single random move. In each move, he rotates either a single dial or two adjacent dials by the same nonzero amount $d$ (where $d\in\{1,2,\ldots,9\}$) in one direction. For example, he can change the lock state from 0 0 1 1 5 to 1 1 1 1 5 by rotating the first two dials by $+1$, but he cannot change it to 1 2 1 1 5 because the two dials must be rotated by the same amount.

After some time, Little Y worries about the security of his locking method. He has recorded $n$ lock states after locking his bicycle (note that none of these states is the correct password).

Your task is to count the number of possible correct passwords $P$ (each a 5‐digit number, with possible leading zeros) such that for every recorded state $S$, there exists a valid move (rotating either a single dial or two adjacent dials by a nonzero amount) which transforms $P$ into $S$. In other words, when comparing $P = p_0p_1p_2p_3p_4$ and a recorded state $S=s_0s_1s_2s_3s_4$, the differences computed modulo $10$ must be all zero except for either exactly one position or exactly two consecutive positions where the difference is the same nonzero value.

inputFormat

The first line contains an integer $n$ ($1\le n\le 100$), the number of recorded states. Each of the next $n$ lines contains a string of 5 digits representing a recorded state of the lock (possibly with leading zeros).

outputFormat

Output a single integer: the number of possible correct passwords that can generate every recorded state via a single valid move.

sample

1
00115

81