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 NONote: the input file will not exceed 1MB.
hide comments
juilee:
20190510 12:13:25
use this property of modulo > (A + B) mod C = (A mod C + B mod C)mod C 

albatross____:
20190501 15:35:58
take long long instead of int. 

hetp111:
20190412 21:20:40
Constrains??! 

hritwik:
20190330 08:01:20
for python3 users, take blank line input as:


randomabraham:
20190317 05:55:47
What are the limits on N and T? 

s106062127:
20190309 16:46:14
Limit should really be offered. We are solving problem, not playing guessing game. 

souravramos04:
20190214 16:47:51
Refer 1st part of this link i.e. Modular Arithmetic as Remainders, you'll get the idea : https://brilliant.org/wiki/modulararithmetic/


abhinav_99:
20190108 19:38:34
use modular division in every iteration otherwise WA


sanchit_aga:
20190106 16:59:11
I have never spent this much time trying to figure out how to take the input. In the end, I read the input line by line in Python3 using 


mukulsingh:
20190104 19:14:24

Added by:  Fudan University Problem Setters 
Date:  20071201 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: C99 ERL JSRHINO 
Resource:  IPSC 2006 