01 Tree

构造一颗具有 $n$ 个叶子结点的带权满二叉树，使得此二叉树具有以下性质： 1. 对于每一个节点，其连向左子的边与连向右子的边，必然有一条权值为 $1$，另一条为 $0$。 2. 令一个叶子结点的点权为其到根节点的简单路径上所有边的边权和。对这颗二叉树进行遍历，第 $i$ 个访问到的叶子结点点权为 $a_i$ 。 对这颗二叉树的遍历伪代码： ``` dfs_order = [] function dfs(v): if v is leaf: append v to the back of dfs_order else: dfs(left child of v) dfs(right child of v) dfs(root) ``` $T$ 组数据。每组数据提供 $n$ 与序列 $a$ 。如果能构造出这颗树，输出 `Yes`，否则输出 `No`。 $T\le10^4 , 2\le n\le 2\times 10^5,0\le a_i \le n-1，\sum n \le2\times10^5$。

There is an edge-weighted complete binary tree with $ n $ leaves. A complete binary tree is defined as a tree where every non-leaf vertex has exactly 2 children. For each non-leaf vertex, we label one of its children as the left child and the other as the right child. The binary tree has a very strange property. For every non-leaf vertex, one of the edges to its children has weight $ 0 $ while the other edge has weight $ 1 $ . Note that the edge with weight $ 0 $ can be connected to either its left or right child. You forgot what the tree looks like, but luckily, you still remember some information about the leaves in the form of an array $ a $ of size $ n $ . For each $ i $ from $ 1 $ to $ n $ , $ a_i $ represents the distance $ ^\dagger $ from the root to the $ i $ -th leaf in dfs order $ ^\ddagger $ . Determine whether there exists a complete binary tree which satisfies array $ a $ . Note that you do not need to reconstruct the tree. $ ^\dagger $ The distance from vertex $ u $ to vertex $ v $ is defined as the sum of weights of the edges on the path from vertex $ u $ to vertex $ v $ . $ ^\ddagger $ The dfs order of the leaves is found by calling the following $ \texttt{dfs} $ function on the root of the binary tree. ``` <pre class="verbatim"><br></br>dfs_order = []<br></br><br></br>function dfs(v):<br></br> if v is leaf:<br></br> append v to the back of dfs_order<br></br> else:<br></br> dfs(left child of v)<br></br> dfs(right child of v)<br></br><br></br>dfs(root)<br></br> ```

Each test contains multiple test cases. The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. The description of the test cases follows. The first line of each test case contains a single integer $ n $ ( $ 2 \le n \le 2\cdot 10^5 $ ) — the size of array $ a $ . The second line of each test case contains $ n $ integers $ a_1, a_2, \ldots, a_n $ ( $ 0 \le a_i \le n - 1 $ ) — the distance from the root to the $ i $ -th leaf. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2\cdot 10^5 $ .

For each test case, print "YES" if there exists a complete binary tree which satisfies array $ a $ and "NO" otherwise. You may print each letter in any case (for example, "YES", "Yes", "yes", "yEs" will all be recognized as a positive answer).

2
5
2 1 0 1 1
5
1 0 2 1 3

YES
NO

In the first test case, the following tree satisfies the array.  In the second test case, it can be proven that there is no complete binary tree that satisfies the array.