An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illustrate the rotation rules.

Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (≤20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated by a space.

Output Specification:

For each test case, print the root of the resulting AVL tree in one line.

Sample Input 1:

5

88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7

88 70 61 96 120 90 65

Sample Output 2:

88

#include<cstdio>

#include<algorithm>

using namespace std;

struct node{

    int v,height;

    node* lchild,*rchild;

}*root;

node* newNode(int v){

    node* Node = new node;

    Node->v = v;

    Node->height = ;

    Node->lchild = Node->rchild = NULL;

    return Node;

}

int getHeight(node* root){

    if(root == NULL) return ;

    return root->height;

}

void updateHeight(node* root){

     root->height = max(getHeight(root->lchild),getHeight(root->rchild)) + ;

}

int getBalanceFactor(node* root){

    return getHeight(root->lchild) - getHeight(root->rchild);

}

void R(node* &root){

    node* temp = root->lchild;

    root->lchild = temp->rchild;

    temp->rchild = root;

    updateHeight(root);

    updateHeight(temp);

    root = temp;

}

void L(node* &root){

    node* temp = root->rchild;

    root->rchild = temp->lchild;

    temp->lchild = root;

    updateHeight(root);

    updateHeight(temp);

    root = temp;

}

void insert(node* &root,int v){

    if(root == NULL){

        root = newNode(v);

        return;

    }

    if(root->v > v){

        insert(root->lchild,v);

        updateHeight(root);

        if(getBalanceFactor(root) == ){

            if(getBalanceFactor(root->lchild) == ){

                R(root);

            }else if(getBalanceFactor(root->lchild) == -){

                L(root->lchild);

                R(root);

            }

        }

    }else{

            insert(root->rchild,v);

            updateHeight(root);

            if(getBalanceFactor(root) == -){

               if(getBalanceFactor(root->rchild) == -){

                L(root);

               }else if(getBalanceFactor(root->rchild) == ){

                R(root->rchild);

                L(root);

               }

           }

        }

}

int main(){

    int n,v;

    scanf("%d",&n);

    for(int i = ; i < n; i++){

        scanf("%d",&v);

        insert(root,v);

    }

    printf("%d",root->v);

    return ;

}