Problem Statement

You are given a sequence of non-negative integers $A=(A_1,A_2,\dots,A_N)$ of length $N$. Here, $S=\sum_{i=1}^{N} A_i$ is even.

Determine whether there is a pair of sequences of non-negative integers of length $N$, $B=(B_1,B_2,\dots,B_N)$ and $C=(C_1,C_2,\dots,C_N)$, that satisfy the following conditions:

• $B_i+C_i=A_i$ for $i=1,2,\dots,N$.
• $\sum_{i=1}^{N} X_i \neq \frac{S}{2}$ for every sequence of integers $X=(X_1,X_2,\dots,X_N)$ of length $N$ where $X_i=B_i$ or $X_i=C_i$ for $i=1,2,\dots,N$.

Solve $T$ test cases.

Constraints

• $1 \leq T$
• $1 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^9$
• $\sum_{i=1}^{N} A_i$ is even.
• The sum of $N$ over all test cases in a single input 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
\mathrm{case}_1
\vdots
\mathrm{case}_T

Each case is given in the following format:

N
A_1 A_2 \dots A_N

Output

Print $T$ lines. The $i$-th line should contain Yes if there is a pair of sequences $B$ and $C$ that satisfy the conditions for the $i$-th test case, and No otherwise.