A binary tree is a tree where each node has at most two children. It is characterized by any of the following properties:
- It can be an empty tree, where root = null.
- It can contain a root node which contain some value and two subtree, left subtree and right subtree, which are also binary tree.
A binary tree is a binary search tree (BST) if all the non-empty nodes follows both two properties:
- Each node's left subtree contains only values less than it, and
- Each node's right subtree contains only values greater than it.
Preorder traversal is a tree traversal method where the current node is visited first, then the left subtree and then the right subtree. More specifically, let's represent the preorder traversal of a tree by a list. Then this list is constructed in following way:
- If the tree is empty, then this list be a null list.
For non-empty tree, let's represent the preorder of left subtree as
L
and of right subtree asR
. Then the preorder of tree is obtained by appendingL
to current node, and then appendingR
to it.1 2 3 \ / \ / \ 3 1 3 2 5 / / / \ 2 1 4 6 (a) (b) (c)
For the above trees, preorder will be
(a) 1 3 2
(b) 2 1 3
(c) 3 2 1 5 4 6
Given a list of numbers, determine whether it can represent the preorder traversal of a binary search tree(BST).
Input
The first line contains the number of test cases, T. Then T test cases follow. The first line of each test case contains the number of nodes in the tree, N. In next line there will a list of N unique numbers, where each number is from set [1, N].
Output
For each test case, print "YES" if there's exist a BST whose preorder is equal to the list otherwise "NO" (without quotes).
Constraints
1 <= T <= 10
1 <= N <= 100
Sample Input
5
3
1 2 3
3
2 1 3
6
3 2 1 5 4 6
4
1 3 4 2
5
3 4 5 1 2
Sample Output
YES
YES
YES
NO
NO
Explanation
First three cases are from examples. And last two test cases are invalid because the subtree for 3 is not valid as 2 and 4 are in the wrong order.