Ice Cream Patrol 

Farmer Maria's farm lies within a village that consists of N fields,
numbered 1..N, (1 <= N <= 1000) connected by M winding paths (1 <= M
<= 10000).  Two fields are of particular interest to FM: field 1, his
farm and field N, the recently-opened Coldstone Ice Cream!

Unfortunately, Farmer Maria has noticed that Bessie is often
disappearing from the farm to visit Coldstone.  Every time she does
this, FM has to follow her footsteps from the farm to Coldstone and
try to catch her red-hooved.  However, Bessie is very clever and takes
a path back from Coldstone that visits entirely different fields along
the way so that FM can't catch her.  (Bessie doesn't want to risk
anything in her path back to the farm, so she cannot use even a single
field she used on the way to Coldstone.)

Before Bessie gets unhealthy, FM wants to place veracious dogs in some
of the fields along the way and prevent Bessie from sneaking out for
midnight treats.  Help FM determine the minimal number of fields he
must guard so that it is impossible for Bessie to travel from the farm
to Coldstone and back without revisiting some field.  (FM cannot guard
either the farm or Coldstone.)

The farm will never be connected to Coldstone by a direct trail.

PROBLEM NAME: patrol

INPUT FORMAT:

* Line 1: Two integers: N and M.

* Lines 2..M+1: Each line contains two integers A and B that describe
        a trail joining fields A and B.  It is possible to travel
        along this trail both ways.  No trail will appear twice.

SAMPLE INPUT (file patrol.in):

6 7
1 2
2 6
1 3
3 4
3 5
4 6
5 6

OUTPUT FORMAT:

* Line 1: A single integer that tells how many fields FM should guard.

SAMPLE OUTPUT (file patrol.out):

1

OUTPUT DETAILS:

FM can guard field 2 (for example).  FM could guard both fields 4 and
5, but that would require more dogs.