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:
$2 \le N \le 10^6$
$1 \le u,v \le N$