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<h1>1123. Is It a Complete AVL Tree (30)</h1>
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<p>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.</p>
<center><img src="http://nos.patest.cn/mr_ohesevgnyny.jpg"/>    <img src="http://nos.patest.cn/mr_ohesfdbkaep.jpg"/></center>
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<center><img src="http://nos.patest.cn/mr_oheseymzi13.jpg"/>    <img src="http://nos.patest.cn/mr_ohesfjddti2.jpg"/></center>
<p>Now given a sequence of insertions, you are supposed to output the level-order traversal sequence of the resulting AVL tree, and to tell if it is a complete binary tree.</p>
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Input Specification:
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<p>Each input file contains one test case.  For each case, the first line contains a positive integer N (&lt;= 20).  Then N distinct integer keys are given in the next line.  All the numbers in a line are separated by a space.</p>
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Output Specification:
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<p>For each test case, insert the keys one by one into an initially empty AVL tree.  Then first print in a line the level-order traversal sequence of the resulting AVL 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.  Then in the next line, print "YES" if the tree is complete, or "NO" if not.
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<b>Sample Input 1:</b><pre>
5
88 70 61 63 65
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<b>Sample Output 1:</b><pre>
70 63 88 61 65
YES
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<b>Sample Input 2:</b><pre>
8
88 70 61 96 120 90 65 68
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<b>Sample Output 2:</b><pre>
88 65 96 61 70 90 120 68
NO
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