Description

A neighborhood arm-wrestling tournament was held. N players joined, and skill follows a strict order, so a stronger player always beats a weaker one. Due to lack of time not every match was played, and only some results were recorded. Luckily, if "A beats B and B beats C", we can be sure A also beats C (because the skill order is consistent). Using only the recorded results, count how many players have their win/loss against every other player fully determined, so their exact rank is decided.

Input

Output

Constraints

• •2 ≤ N ≤ 100
• •0 ≤ M ≤ N×(N-1)/2
• •No contradictions (cycles) in the given results

Examples

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

3