Knights

A knight attacks the squares shown in the figure below (the knight on square $S$ attacks the squares marked with a cross).

You are given a chessboard of size $3 \times n$ with 3 rows and $n$ columns, where $1 \le n \le 100$, together with a set $Z$ of blocked squares. Rows are numbered from top to bottom as $1$ through $3$, and columns from left to right as $1$ through $n$.

Knights may be placed only on squares that are not in $Z$, and no two placed knights may attack each other. At most one square in each column belongs to $Z$. The set $Z$ is given by a sequence $k_1, k_2, \ldots, k_n$ with each $k_i \in \{0, 1, 2, 3\}$: if $k_i = 0$ then no square in column $i$ is blocked, otherwise $k_i$ is the row index of the single blocked square in column $i$.

Compute the maximum number of knights $M$ that can be placed under these rules, and $L$, the number of distinct placements of exactly $M$ knights.

The first line contains one integer $n$ ($1 \le n \le 100$), the number of columns. Each of the next $n$ lines contains one integer from $\{0, 1, 2, 3\}$, giving the terms $k_1, k_2, \ldots, k_n$ that describe $Z$.

Print two integers $M$ and $L$ separated by a single space: the maximum number of knights, and the number of placements that achieve this maximum.