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There are several outdoor movie sets in Beykoz Kundura, each of which consist of several streets and their intersections. Specifically, each street connects 2 intersections.
In order to secure these movie sets, and remove any fans snooping around, security guards are going to be placed in certain intersections of every set.
A security guard placed at an intersection A can cover all the intersections adjacent to A. (and the streets between intersection A and those neighboring intersections) Being a chatty bunch, however, if a street is covered by more than 1 security guards, they start chatting with one another and miss any movie fans walking around the set. Kundura is fun and all, but chatty security guards are not allowed to work in here!
Given the information about the movie sets and about the security guards, it is time to give back to the Kundura community! Help them find out the minimum number of total security guards required to cover every part of each outdoor movie set.
Input Format
The first line contains 2 integers I and S, indicating the total number of intersections and streets in the movie sets of Beykoz Kundura.
Each of the next S lines contains 2 integers a and b, denoting that there is a street between the intersections with index a and b.
Constraints
The intersections are 1-indexed.
1 <= I <= 200
1 <= S <= 10000
1 <= a, b <= I
Output Format
Print an integer denoting the minimum number of security guards required. If it is impossible to place the security guards so that none of them chat with each other, print -1.
Sample Input 0
4 2
1 2
3 4
Sample Output 0
2
Sample Input 1
5 5
1 2
2 3
3 4
1 5
4 5
Sample Output 1
-1
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