Problem Statement

You are given a positive integer $N$ and a permutation $P$ of $(1,2,\dots,N)$.

When there is a tree with $N$ vertices numbered $1,2,\dots,N$, Snuke and Takahashi move according to the following rules:

• Snuke specifies a permutation $Q$ of $(1,2,\dots,N)$ such that the sequence returned by Takahashi, when following the rules below, is lexicographically maximum.
• Takahashi, who is at vertex $1$ of the tree, first receives $Q$ from Snuke and initializes an integer sequence $R$ with the length-$1$ sequence $(Q_1)$. Then, he moves $N-1$ times as follows, and returns the final $R$:
• Visit the vertex $i$ with the smallest $Q_i$ among vertices that are adjacent to a previously visited vertex but have not yet been visited (it can be proved that there is always exactly one such vertex). Then, append $Q_i$ to the end of $R$.

Here, vertex $1$ is considered to have been visited initially.

Determine whether there exists a tree such that Takahashi returns $P$.

You are given $T$ test cases; solve each of them.

Constraints

• $1 \le T \le 10^5$
• $1 \le N \le 2 \times 10^5$
• $P$ is a permutation of $(1,2,\dots,N)$.
• The sum of $N$ over all test cases is at most $2 \times 10^5$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

T
\text{case}_1
\text{case}_2
\vdots
\text{case}_T

Each test case is given in the following format:

N
P_1 P_2 \ldots P_N

Output

Output $T$ lines.

The $i$-th line should contain Yes if there exists a tree satisfying the conditions for the $i$-th test case, and No otherwise.