# Floyd - Warshall + Transitive closure

# Cow Contest

**n** cows, conveniently numbered **1**..**n**, are participating in a programming contest. As we all know, some cows code better than others. Each cow has a certain constant skill rating that is unique among the competitors.

The contest is conducted in several head-to-head rounds, each between two cows. If cow **a** has a greater skill level than cow **b** (**1** ≤ **a**, **b** ≤ **n**, **a** ≠ **b**), then cow **a** will always beat cow **b**.

Farmer John is trying to rank the cows by skill level. Given a list the results of **m** two-cow rounds, determine the number of cows whose ranks can be precisely determined from the results. It is guaranteed that the results of the rounds will not be contradictory.

#### Input

First line contains two integers **n** (**1** ≤ **n** ≤ **100**) and **m** (**1** ≤ **m** ≤ **4500**). Each of the next **m** lines contains two space-separated integers that describe the competitors and results (the first integer **a**, is the winner) of a single round of competition: **a** and **b**.

#### Output

Print a single integer representing the number of cows whose ranks can be determined.

5 5 4 3 4 2 3 2 1 2 2 5

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