## Problem solution codechef

*Believe nothing you hear, and only one half that you see*

On a Halloween evening, young Tim embarks on a candy-filled quest with his friends, dressed as ghouls and witches.

There are $N$ friends, initially the $i$-th of them has $A_{i}$ candies.

To truly savor the spooky spirit, Tim wishes for everyone to have an **equal** number of candies.

To achieve this, he is armed with a magical operation which is as follows:

- First, Tim chooses two integers $i$ and $j$ ($1≤i,j≤N$), denoting the indices of two of his friends.
- Next, he chooses an integer $k$ that’s
**at least $1$**, while also satisfying $_{k}≤A_{i}$.

That is, the inequality $2≤_{k}≤A_{i}$ should hold. - Finally, Tim takes away $_{k}$ candies from friend $i$ and gives them to the friend $j$.

That is, their candy counts change to $(A_{i}−_{k})$ and $(A_{j}+_{k})$ respectively.

Determine whether all of Tim’s friends can have an equal number of candies in the end, after some (possibly zero) operations are performed.

### Input Format

- The first line of input will contain a single integer $T$, denoting the number of test cases.
- Each test case consists of two lines of input.
- The first line of each test case contains an integer $N$ — the number of friends.
- The next line contains $N$ space-separated integers $A_{1},A_{2},…,A_{N}$ — the initial number of candies each friend has.

### Output Format

For each test case output the answer on a new line — `"Yes"`

(without quotes) if it is possible to perform operations such that in the end all friends have same number of candies, and `"No"`

(without quotes) otherwise.

Each letter of the output may be printed in either uppercase or lowercase, i.e, `"Yes"`

, `"YES"`

, and `"yEs"`

will all be treated as equivalent.

### Constraints

- $1≤T≤1_{3}$
- $1≤N≤1_{5}$
- $1≤A_{i}≤1_{3}$
- The sum of $N$ over all test cases does not exceed $3⋅1_{5}$

### Sample 1:

3 2 4 4 3 2 4 12 2 4 6

Yes Yes No

### Explanation:

**Test case $1$:** No operations are required, everyone already has an equal number of candies.

**Test case 2:** Consider the following sequence of operations:

- Move $_{2}=4$ candies from friend $3$ to friend $1$. The candy counts are now $[6,4,8]$.
- Move $_{1}=2$ candies from friend $3$ to friend $2$. The candy counts are now $[6,6,6]$.

Everyone has an equal number of candies now, as required.

**Test case $3$:** There is no way to perform operations to have all friends with same number of candies