Counting Food Chains in an Ecosystem

In an ecosystem, the food web describes the energy flow among different species. Given n species numbered from 1 to n and m energy flow relationships, you are to count the number of food chains. Each energy flow is given as a pair of numbers a_i and b_i (for i = 1, 2, \ldots, m), indicating that energy flows from species a_i to species b_i. Note that a species that is isolated (i.e. not involved in any energy flow) does not constitute a food chain. In other words, only components having at least two species (directly or indirectly connected via energy flows) form a valid food chain.

Definition:

• Consider an undirected connection between two species if there is an energy flow (in either direction) between them.
• A food chain is defined as a connected component (under the undirected interpretation) that contains at least two species.
• Your task is to count such connected components.
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inputFormat

The first line contains two integers n and m (1 ≤ n ≤ 10⁵, 0 ≤ m ≤ 10⁵), representing the number of species and the number of energy flow relationships respectively.

The second line contains 2*m integers: a₁ b₁ a₂ b₂ \ldots a_m b_m, where each pairing represents an energy flow from species a_i to species b_i.

outputFormat

Output a single integer representing the number of food chains (i.e. the number of connected components with at least two species) in the ecosystem.

sample

5 3
1 2 2 3 4 5

2