$N$ $(1 \le N \le 100)$ 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 $B$ $(1 \le A \le N; 1 \le B \le N; A \ne B)$, 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 $M$ $(1 \le M \le 4,500)$ 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

Read the input from standard input.

• Line 1: Two space-separated integers: $N$ and $M$
• Lines $2..M+1$: Each line 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

Write the output to standard output.

• Line 1: A single integer representing the number of cows whose ranks can be determined

Examples

Input 1

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

Output 1

2

Cow 2 loses to cows 1, 3, and 4. Thus, cow 2 is no better than any of the cows 1, 3, and 4. Cow 5 loses to cow 2, so cow 2 is better than cow 5. Thus, cow 2 must be fourth, and cow 5 must be fifth. The ranks of the other cows cannot be determined.

Problem credits: Neal Wu, 2007