/*
f[i] stands for subtree with root being i
f[i][0] stands for tower needed to cover the whole tree using i
f[i][1] stands for tower needed to cover the whole tree wihout using i
f[i][2] stands for tower needed to cover the tree except i
then we have:
f[r][2] = sum{f[c][1]}, where c is child of r <= cover all subtrees without using subtree root
f[r][0] = 1 + sum{min(f[c][0], f[c][1], f[c][2])}
f[r][1] = choose one child k use f[k][0], then sum up other children min(f[i][0], f[i][1])
*/