You have been given a tree consisting of N nodes. Lets consider two pivot nodes in this tree, A and B such that A and B are not equal. For any node u, lets define \(PivotDistance(u\)) to be minimum of shortest path distance of u from A and B. Thus \(PivotDistance(u\)) = \(min(dist(u,A), dist(u, B))\) where \(dist(u,A)\) is the shortest path distance of u from A and \(dist(u,B)\) is the shortest path distance of u from B. Note that if u is equal to A or B, then \(PivotDistance(u\)) will be 0.

Now consider \(PivotDistance(u)\) for all the nodes u in this tree and define \(maxPivotDistance\) to be maximum value of \(PivotDistance(u)\) for all the nodes u in the tree.

You don't like the higher value of this quantity \(maxPivotDistance\). So you want to minimise the value of \(maxPivotDistance\) by choosing the two pivot nodes A and B optimally. Find two pivot nodes A and B for which the value of \(maxPivotDistance\) is minimum.

INPUT:
First line will consists of integer N denoting total number of nodes in tree. Next \(N-1\) lines will consists of two integers u and v denoting edge between nodes u and v.

OUTPUT:
First line of output should consists of the minimum value of \(maxPivotDistance\) that can be obtained by choosing pivot nodes A and B optimally.
Next line of output should consists of two distinct pivot nodes A and B that gives the minimum possible value of \(maxPivotDistance\). If there are many such possible pairs, print any one of them.

CONSTRAINTS:
\(2 \le N \le 10^6\)
\(1 \le u,v \le N\)