Equal Range Partition - Repovive Opening Round | Repovive

0C. Equal Range Partition

1500 pts2s256 MB

You are given an integer array $a$ of length $n$ . Determine whether it is possible to partition the elements into two non-empty subsets $S_1$ and $S_2$ (each element goes to exactly one subset) such that:

$(\max(S_1) - \min(S_1)) = (\max(S_2) - \min(S_2))$

Note: A single-element subset has range $0$ (since $\max = \min$ ).

For each test case, output Yes if such a partition exists, otherwise output No.

Note: The judge is case-sensitive. Only exactly "Yes" or "No" will be accepted.

Constraints

$1 \le t \le 2 \times 10^5$
$2 \le n \le 2 \times 10^5$
$-10^9 \le a_i \le 10^9$
The sum of $n$ over all test cases does not exceed $2 \times 10^5$ .

Input

t \\[0.5em] \left. \begin{array}{l} n \\ a_1 \quad a_2 \quad \cdots \quad a_n \end{array} \right\} \times t

Output

\begin{array}{l} ans_1 \\ \vdots \\ ans_t \end{array}

Where each answer is exactly "Yes" or "No" (case-sensitive).

Samples

Input

Explanation

Sample 1: [3,1,5,2,4] Yes (S1={1,4}, S2={2,3,5}, ranges 3,3). Sample 2: [2,1,3,2] Yes (S1={1,2}, S2={2,3}, ranges 1,1). Sample 3: [5,1,2] No (no valid partition). Sample 4: [2,1] Yes (S1={2}, S2={1}, both single-element subsets have range 0).

Output

Yes
Yes
No
Yes

$(\max(S_1) - \min(S_1)) = (\max(S_2) - \min(S_2))$

Note: A single-element subset has range $0$ (since $\max = \min$ ).

For each test case, output Yes if such a partition exists, otherwise output No.

Note: The judge is case-sensitive. Only exactly "Yes" or "No" will be accepted.

Constraints

$1 \le t \le 2 \times 10^5$
$2 \le n \le 2 \times 10^5$
$-10^9 \le a_i \le 10^9$
The sum of $n$ over all test cases does not exceed $2 \times 10^5$ .

t \\[0.5em] \left. \begin{array}{l} n \\ a_1 \quad a_2 \quad \cdots \quad a_n \end{array} \right\} \times t

\begin{array}{l} ans_1 \\ \vdots \\ ans_t \end{array}

Where each answer is exactly "Yes" or "No" (case-sensitive).

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0C. Equal Range Partition

Input

Output

Samples

0C. Equal Range Partition

Constraints

Input

Output

Samples

Constraints