A Binary Search Tree (BST) is recursively defined as a binary tree which has the following properties:

• The left subtree of a node contains only nodes with keys less than the node's key.
• The right subtree of a node contains only nodes with keys greater than or equal to the node's key.
• Both the left and right subtrees must also be binary search trees.

A Complete Binary Tree (CBT) is a tree that is completely filled, with the possible exception of the bottom level, which is filled from left to right.

Now given a sequence of distinct non-negative integer keys, a unique BST can be constructed if it is required that the tree must also be a CBT. You are supposed to output the level order traversal sequence of this BST.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=1000). Then N distinct non-negative integer keys are given in the next line. All the numbers in a line are separated by a space and are no greater than 2000.

Output Specification:

For each test case, print in one line the level order traversal sequence of the corresponding complete binary search tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line.

Sample Input:

10

1 2 3 4 5 6 7 8 9 0

Sample Output:

6 3 8 1 5 7 9 0 2 4

 #include<cstdio>

 #include<stack>

 #include<algorithm>

 #include<iostream>

 #include<stack>

 #include<set>

 #include<map>

 #include<cmath>

 using namespace std;

 int line[],tree[];

 void Build(int *line,int *tree,int n,int cur){

     if(!n){

         return;

     }

     int h=log(n)/log();

     int x=n-(pow(,h)-);

     //cout<<"x: "<<x<<endl;

     if(x>pow(,h-)){

        x=pow(,h-);

     }

     //cout<<"x: "<<x<<endl;

     int l=pow(,h-)+x-;

     //cout<<"l:  "<<l<<endl;

     tree[cur]=line[l];

     Build(line,tree,l,cur*+);

     Build(line+l+,tree,n-l-,cur*+);

 }

 int main(){

     //freopen("D:\\INPUT.txt","r",stdin);

     int n,i;

     scanf("%d",&n);

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

         scanf("%d",&line[i]);

     }

     sort(line,line+n);

     Build(line,tree,n,);

     printf("%d",tree[]);

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

         printf(" %d",tree[i]);

     }

     printf("\n");

     return ;

 }