/** This class implements AVL tree. **/
import java.io.*;
import java.lang.*;
import java.util.*;

class Tree {
  AVL root_=null;

  public Tree(){}

  void dump () {
    if (root_!= null)
      root_.dump(5);
  }
  void remove (Comparable o) { 
    if (root_!= null) {
      root_=root_.remove(o);
      if (root_!= null) root_.shorter_=false;
    }
  }
  void add (Comparable o) { 
    if (root_== null)
      root_=new AVL(o);
    else {
      root_=root_.insert(o);
      root_.taller_=false;
    }
  }
  Object find (Comparable o) { 
    if (root_== null)
      return null;
    else {
      return root_.find(o);
    }
  }
  boolean validate () {
    //if the tree is empty, its valid.
    if (root_== null)
      return true;

    //if any nodes Balance Factor starting with the root is invalid, 
    //return false; otherwise, continue validation.
    if (!root_.BFisOK()) return false;

    //element in root must be bigger than all elements in its left subtree and
    //smaller than those to its right. The same is true for every node
    //in our tree. Validate and return true if all is well; otherwise, 
    //return false.
    if (root_.left_ != null && 
        !root_.left_.keyOK(root_.element_,true)) return false;

    if (root_.right_ != null &&
        !root_.right_.keyOK(root_.element_,false)) return false;

      return true;
  }
}