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<iostream>
#include<cstdio>
#include<algorithm>
#include<cmath>																							
#include<vector>
#include<queue>
#include<cstring>
#include<stack>
using namespace std;
const int maxn = 110;
struct node {
	int data,h;
	node* lchild;
	node* rchild;
};
node *newnode(int v) {
	node *Node = new node;
	Node->data = v;
	Node->h = 1;
	Node->lchild = NULL;
	Node->rchild = NULL;
	return Node;
}
int geth(node* root) {
	if (root == NULL) return 0;
	return root->h;
}
int getb(node* root) {
	return geth(root->lchild) - geth(root->rchild);
}
void updateh(node* root) {
	root->h = max(geth(root->lchild), geth(root->rchild)) + 1;
}
void R(node* &root) {
	node* tmp = root->lchild;
	root->lchild = tmp->rchild;
	tmp->rchild = root;
	updateh(root);
	updateh(tmp);
	root = tmp;
}
void L(node* &root) {
	node* tmp = root->rchild;
	root->rchild = tmp->lchild;
	tmp->lchild = root;
	updateh(root);
	updateh(tmp);
	root = tmp;
}
void insert(node* &root, int v) {
	if (root == NULL) {
		root = newnode(v);
		return;
	}
	if (v < root->data) {
		insert(root->lchild, v);
		updateh(root);
		if (getb(root) == 2) {
			if (getb(root->lchild) == 1) {
				R(root);
			}
			else if (getb(root->lchild) == -1) {
				L(root->lchild);
				R(root);
			}
		}
	}
	else {
		insert(root->rchild, v);
		updateh(root);
		if (getb(root) == -2) {
			if (getb(root->rchild) == -1) {
				L(root);
			}
			else if (getb(root->rchild) == 1) {
				R(root->rchild);
				L(root);
			}
		}
	}
}
int main() {
	int n,k;
	scanf("%d", &n);
	node *root = NULL;
	for (int i = 0; i < n; i++) {
		scanf("%d", &k);
		insert(root, k);
	}
	printf("%d", root->data);
	return 0;
}