Wisconsin has had an earthquake that has struck Farmer John's farm! The earthquake has damaged some of the pastures so that they are unpassable. Remarkably, none of the cowpaths was damaged.
As usual, the farm is modeled as a set of P (1 <= P <= 3,000) pastures conveniently numbered 1..P which are connected by a set of C (1 <= C <= 20,000) non-directional cowpaths conveniently numbered 1..C. Cowpath i connects pastures a_i and b_i (1 <= a_i <= P; 1 <= b_i <= P). Cowpaths might connect a_i to itself or perhaps might connect two pastures more than once. The barn is located in pasture 1.
A total of N (1 <= N <= P) cows (in different pastures) sequentially contacts Farmer John via moobile phone with an integer message report_j (2 <= report_j <= P) that indicates that pasture report_j is undamaged but that the calling cow is unable to return to the barn from pasture report_j because she could not find a path that does not go through damaged pastures.
After all the cows report in, determine the minimum number of pastures that are damaged.