Pearls

Problem Background

Special for beginners, ^_^

Problem Description

There are $n$ pearls that are identical in shape and size, but their weights are all different. $n$ is an integer, and all the pearls are numbered from $1$ to $n$. Your task is to find out which pearl has exactly the middle weight, i.e. its weight ranks $(n+1)/2$-th among all the pearls' weights. The following is a way to compare a pair of pearls:

You are given a balance to compare the weights of pearls; we can tell which of two pearls is heavier. After a series of comparisons, we can remove some pearls that definitely do not have the middle weight.

For example, the following shows four comparisons on $5$ pearls:

1. Pearl $2$ is heavier than pearl $1$;
2. Pearl $4$ is heavier than pearl $3$;
3. Pearl $5$ is heavier than pearl $1$;
4. Pearl $4$ is heavier than pearl $2$.

From the above results, although we cannot precisely find which pearl has the middle weight, we can be sure that pearl $1$ and pearl $4$ cannot have the middle weight, because pearls $2, 4, 5$ are heavier than pearl $1$, while pearls $1, 2, 3$ are lighter than pearl $4$, so we can remove these two pearls.

Write a program to count how many pearls are definitely not of middle weight.

Input Format

The first line of input contains two integers separated by a space: $N$ and $M$, where $1 \le N \le 99$ and $N$ is odd. $M$ is the number of comparisons made on the pearls. The following $M$ lines each contain two integers separated by a space: $x$ and $y$, meaning pearl $x$ is heavier than pearl $y$.

Output Format

Output a single line containing one integer: the total number of pearls that cannot be of middle weight.

Sample Input

123 500

Sample Output

623

Constraints

Time limit: 1s; memory limit: 1024 KiB for each test case.