Problem Description

For a sequence $c$, define the range of $c$ as the difference between the maximum value and the minimum value in $c$. Now you are given a sequence $a$ of length $n$. Determine whether it is possible to split it into at least two subsequences, each of length greater than $1$, such that the range of every subsequence is equal (note that all elements must be assigned, and each element can be assigned to only one subsequence).

Input Format

This problem contains multiple test cases.

The first line contains two integers $T,id$, representing the number of test cases and the subtask ID.

For each test case:

The first line contains a positive integer $n$, representing the length of the array.

The second line contains $n$ integers representing the sequence $a$.

Output Format

For each test case, output one line containing a string Yes or No.

2 1
6
1 1 4 5 1 4
7
1 9 1 9 8 1 0

No
Yes

Hint

Explanation for Sample $\small\text{1}$

The sample satisfies the constraints of Subtask 1, with $id=1$.

Query 1:

It can be proven that no solution satisfies the conditions.

Query 2:

One valid set of subsequences is:

• $\{1,9\}$.
• $\{1,9\}$.
• $\{8,1,0\}$.

The answer is not unique.

Constraints

This problem uses bundled testdata.

• Subtask 1 (20 points): $4\le \sum n\le 20,a_i\ge 0$.
• Subtask 2 (20 points): $4\le \sum n\le 100,a_i\ge 0$.
• Subtask 3 (20 points): $4\le \sum n\le 10^3,a_i\ge 0$.
• Subtask 4 (10 points): all elements in array $a$ are equal.
• Subtask 5 (30 points): no special restrictions.

For $100\%$ of the testdata, $4\le \sum n\le 10^6,0\le |a_i|\le 10^9,1\le T\le 300$.

Translated by ChatGPT 5