Kattis

# Forests

If a tree falls in the forest, and there’s nobody there to hear, does it make a sound? This classic conundrum was coined by George Berkeley (1685-1753), the Bishop and influential Irish philosopher whose primary philosophical achievement is the advancement of what has come to be called subjective idealism. He wrote a number of works, of which the most widely-read are Treatise Concerning the Principles of Human Knowledge (1710) and Three Dialogues between Hylas and Philonous (1713) (Philonous, the “lover of the mind,” representing Berkeley himself).

A forest contains $T$ trees numbered from $1$ to $T$ and $P$ people numbered from $1$ to $P$. People may have different opinions as to which trees, according to Berkeley, have made a sound. Given who has heard which trees fall, how many different opinions are there? Two people hold the same opinion only if they hear exactly the same set of trees.

## Input

Standard input consists of a line containing $1 \le P < 100$ and $1 \le T < 100$ followed by at most $T \cdot P$ lines (terminated by end-of-file), each containing a pair of integers $i$ and $j$, indicating that person $i$ has heard tree $j$ fall. No pair $i$ and $j$ appears more than once.

## Output

Output the number of different opinions represented in the input.

Sample Input 1 Sample Output 1
3 4
1 2
3 3
1 3
2 2
3 2
2 4

2