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 ythe 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<stdio.h>
#include<vector>
#include<algorithm>
using namespace std; struct node
{
node(int v):left(NULL),right(NULL),high(),val(v){}
node* left,* right;
int val,high;
}; int gethigh(node* root)
{
int a = , b = ;
if(root->left!= NULL)
a = root->left->high;
if(root->right!= NULL)
b = root->right->high;
return a > b ? a+:b+;
} void R(node* & root)
{
node* tem = root->left;
root->left = tem->right;
tem->right = root;
root->high = gethigh(root);
tem->high = gethigh(tem);
root = tem;
} void L(node* & root)
{
node* tem = root->right;
root->right = tem->left;
tem->left = root;
root->high = gethigh(root);
tem->high = gethigh(tem);
root = tem;
} void insert(node*& root,int val)
{
if(root == NULL)
{
root = new node(val);
return;
} if(val < root->val)
{
insert(root->left,val);
root->high = gethigh(root);
int a = root->left == NULL ? : root->left->high;
int b = root->right == NULL ? : root->right->high;
if(a - b == )
{
int c = root->left->left == NULL ? :root->left->left->high;
int d = root->left->right == NULL ? :root->left->right->high;
if(c - d == )
{
R(root);
}
else if(c - d == -)
{
L(root->left);
R(root);
}
}
}
else
{
insert(root->right,val);
root->high = gethigh(root);
int a = root->left == NULL ? : root->left->high;
int b = root->right == NULL ? : root->right->high;
if(a - b == -)
{
int c = root->right->right == NULL ? :root->right->right->high;
int d = root->right->left == NULL ? :root->right->left->high;
if(c - d == )
{
L(root);
}
else if(c - d == -)
{
R(root->right);
L(root);
}
}
}
} int main()
{
int n,tem;
scanf("%d",&n);
node* Tree = NULL;
for(int i = ;i < n;++i)
{
scanf("%d",&tem);
insert(Tree,tem);
}
printf("%d\n",Tree->val);
return ;
}

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