L. Integer Average
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given an array $$$a$$$ of length $$$n$$$ consisting of positive integers.

The average of a sequence $$$b$$$ of length $$$m$$$ is equal to $$$\frac{b_1 \text{ } + \text{ } b_2 \text{ } + \text{ } \dots \text{ } + \text{ } b_m}{m}$$$. Note that the average is not necessarily an integer.

A sequence $$$c$$$ is considered a subsequence of $$$a$$$ if we can obtain $$$c$$$ by removing some elements (possibly zero) from $$$a$$$ (not necessarily adjacent elements). For example, [$$$1$$$], [$$$1$$$, $$$3$$$] and [$$$1$$$, $$$2$$$, $$$4$$$, $$$6$$$, $$$1$$$, $$$3$$$] are all subsequences of [$$$1$$$, $$$2$$$, $$$3$$$, $$$4$$$, $$$5$$$, $$$6$$$, $$$9$$$, $$$1$$$, $$$3$$$].

Your task is to find if there exists any subsequence of $$$a$$$ consisting of at least 2 elements, such that the average of this subsequnce is an integer.

Input

The first line of the input contains a single integer $$$t$$$ ($$$1 \le t \le 10^3$$$) — representing the number of testcases.

The first line of each testcase contains a single integer $$$n$$$ ($$$2 \le n \le 10^5$$$) — representing the size of the array.

The second line of each testcase contains $$$n$$$ space-separated integers $$$a_1, a_2, ..., a_n$$$ ($$$1 \le a_i \le 10^9$$$) — representing the elements of the array.

It's guaranteed the sum of $$$n$$$ over all testcases doesn't exceed $$$10^5$$$.

Output

For each testcase, print a new line containing a single word — YES if the answer exists and NO otherwise. The checker is not case-sensitive, meaning that responses like Yes, yES and yes will be considered positive responses and responses like No, nO and no will be treated as negative responses.

Example
Input
2
2
6 5
7
10 9 8 7 6 5 4
Output
NO
YES