B. Closed by Subtraction
time limit per test
3 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

We say that a set of integers is closed by subtraction if, for every pair of distinct numbers in the set $$$a, b$$$, at least one of the two values $$$(a-b)$$$, $$$(b-a)$$$ also belongs to the set.

Given a set of integers, determine if it is closed by subtraction.

Input

The first line contains an integer $$$T$$$, the number of test cases.

For each case, there is a line with an integer $$$n$$$, the number of elements in the set, followed by another line with $$$n$$$ integers $$$a_1, \ldots, a_n$$$, the numbers in the set. The $$$a_i$$$ are all distinct.

Output

For each case, write a line with "SI" if the set is closed by subtraction and "NO" otherwise.

Scoring

$$$1 \leq T \leq 100$$$.

$$$2 \leq n \leq 5 \cdot 10^5$$$, the sum of $$$n$$$ for all cases is less than $$$2 \cdot 10^6$$$.

$$$-10^9 \leq a_i \leq 10^9$$$ for $$$1 \leq i \leq n$$$.

40 points: $$$n \leq 100$$$, the sum of $$$n$$$ for all cases is less than $$$2000$$$.

25 points: $$$n \leq 2000$$$, the sum of $$$n$$$ for all cases is less than $$$2 \cdot 10^4$$$.

35 points: No additional restrictions.

Example
Input
5
3
1 2 3
4
5 4 0 2
3
-1 0 1
5
-4 -2 -6 -10 -8
2
1000000000 0
Output
SI
NO
NO
SI
SI