CANDY3 - Candy III

A class went to a school trip. And, as usually, all N kids have got their backpacks stuffed with candy. But soon quarrels started all over the place, as some of the kids had more candies than others. Soon, the teacher realized that he has to step in: "Everybody, listen! Put all the candies you have on this table here!"

Soon, there was quite a large heap of candies on the teacher's table. "Now, I will divide the candies into N equal heaps and everyone will get one of them." announced the teacher.

"Wait, is this really possible?" wondered some of the smarter kids.

Problem specification

You are given the number of candies each child brought. Find out whether the teacher can divide the candies into N exactly equal heaps. (For the purpose of this task, all candies are of the same type.)

Input specification

The first line of the input file contains an integer T specifying the number of test cases. Each test case is preceded by a blank line.

Each test case looks as follows: The first line contains N : the number of children. Each of the next N lines contains the number of candies one child brought.

Output specification

For each of the test cases output a single line with a single word "YES" if the candies can be distributed equally, or "NO" otherwise.

Example

```Input:
2

5
5
2
7
3
8

6
7
11
2
7
3
4

Output:
YES
NO
```
Note: the input file will not exceed 1MB.

hide comments
 Mateusz Drewienkowski: 2011-06-19 20:52:02 I think the number of candies could be quite large. Too bad, there is no proper specification. sreenatha: 2011-05-12 17:40:48 for those still stuck , u can't just add all the values and store it in a long long int . Hint : Use Modular Arithmetic Krzysztof Lewko: 2011-05-02 14:15:44 this problem is weirdo as hell. Use modulo trick and LONG LONG. S: 2011-04-14 06:30:37 for those who need the range: dont sum up all candies if u do long long in c is not enough else u should get ac (atleast for long long) Krzysztof Butkiewicz: 2011-03-21 02:15:24 max N ? max sum of candies? we've got useless story here but we don't have the basic range information... Stefan: 2011-02-19 17:17:03 How many tons example we can have? 2 3 4 5 6 YES 7 6 5 43 23 4 5 6 NO This is it true? ~!(*(@*!@^&: 2010-04-19 03:06:55 Hi, i am the 1234th people who AC this problem ^^.

 Added by: Fudan University Problem Setters Date: 2007-12-01 Time limit: 1s Source limit: 50000B Memory limit: 1536MB Cluster: Cube (Intel G860) Languages: All except: C99 ERL JS-RHINO Resource: IPSC 2006