Each of Farmer John's N cows (1 <= N <= 1,000) produces milk at a different positive rate, and FJ would like to order his cows according to these rates from the fastest milk producer to the slowest.</p>

FJ has already compared the milk output rate for M (1 <= M <= 10,000) pairs of cows.  He wants to make a list of C additional pairs of cows such that, if he now compares those C pairs, he will definitely be able to deduce the correct ordering of all N cows.  Please help him determine the minimum value of C for which such a list is possible.

입력 형식

• Line 1: Two space-separated integers: N and M
• Lines 2..M+1: Two space-separated integers, respectively: X and Y. Both X and Y are in the range 1...N and describe a comparison where cow X was ranked higher than cow Y.
</ul>

 

## 출력 형식
• Line 1: A single integer that is the minimum value of C.

예제 입력

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

예제 출력

3

힌트

FJ is comparing 5 cows and has already determined that cow 2 > cow 1, cow 1 > cow 5, cow 2 > cow 3, cow 1 > cow 4, and cow 3 > cow 4 (where the '>' notation means "produces milk more quickly").</p>

From the information in the 5 test results, Farmer John knows that since cow 2 > cow 1 > cow 5 and cow 2 > cow 3 > cow 4, cow 2 has the highest rank. However, he needs to know whether cow 1 > cow 3 to determine the cow with the second highest rank. Also, he will need one more question to determine the ordering between cow 4 and cow 5. After that, he will need to know if cow 5 > cow 3 if cow 1 has higher rank than cow 3. He will have to ask three questions in order to be sure he has the rankings: "Is cow 1 > cow 3?  Is cow 4 > cow 5? Is cow 5 > cow 3?"