The 3rd IUPC

IUPC (International University student Product Contest) is a contest where teams of three compete on how fast and how accurately they multiply large numbers. Inha University took the grand prize at the first contest with the team "I inha U", and again at the second contest with the team "URF". The third IUPC is held today.

The day is a happy one, but the competing teams are uneasy. CTP, which runs the contest, decided that Inha University winning every time hurts the morale of the other universities, so it changed the rules.

The old contest was simple: two large numbers were given and a team multiplied them as fast as it could. The third IUPC runs as follows.

1. $A$, $B$ and $C$ are given in order on $N$ lines.
2. Call the values on line $i$ by the names $A_i$, $B_i$ and $C_i$. For every $i$, compute $A_i \times B_i^0$, $A_i \times B_i^1$, $A_i \times B_i^2$, $\dots$, $A_i \times B_i^{C_i}$ and write each result on its own card.
3. Once all the multiplications are done there are $\sum_{i=1}^{N}{(C_i+1)}$ cards. Gather the cards that carry the same number into one group.
4. After the grouping there are $K$ groups. $K$ can equal the number of cards or be smaller than it. The team that computes $K$ first wins.

The first line contains $N$ ($1 \le N \le 100$). Each of the next $N$ lines contains $A_i$, $B_i$ and $C_i$ separated by spaces. ($2 \le A_i, B_i \le 100{,}000$, $1 \le C_i \le 100{,}000$)

Print $K$, the number of groups formed when the cards are sorted by the rules above, on the first line.