Tiling Up Blocks

Michael the Kid got a game set from his grandparent as a birthday gift. The box holds $n$ tiling blocks, and every block has the shape below.

Figure 1: a tiling block with parameters $(3, 2)$.

Every block carries two parameters $(\ell, m)$. The upper face has $\ell$ protruding knobs on the left and $m$ protruding knobs in the middle, and the bottom face is carved with $\ell$ dens on the left and $m$ dens in the middle at the matching spots.

An $(\ell, m)$ block clearly sits on another $(\ell, m)$ block, and that is not the only legal placement. An $(\ell, m)$ block can be tiled upon an $(\ell', m')$ block if and only if $\ell \ge \ell'$ and $m \ge m'$.

You are given a box $B = \{b_1, b_2, \dots, b_n\}$ of $n$ blocks, where block $b_i$ has parameters $(\ell_i, m_i)$. Report how many blocks the tallest tower built from $B$ contains.

The input lists several game boxes back to back. Each box starts with the integer $n$, the number of blocks inside it. The next $n$ lines each hold two integers, the left parameter $\ell_i$ and the middle parameter $m_i$ of the $i$-th block.

$n$ is at most $10\,000$, and $\ell_i$ and $m_i$ lie between $1$ and $100$. A value of $n = 0$ marks the end of the input.

For each box, print on its own line how many blocks the tallest tower built from that box contains. After the last box, print a single star * on a line of its own.