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.

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

hide comments
2015-04-02 04:15:47 Justin Roberts
Problem is trivial with Python. I didn't even get the point of it until I read the comments. Languages should be limited to those that don't play with large numbers so nicely.
2015-03-19 21:58:02 burninggoku
DFS,BFS
2015-03-09 22:34:35 Tirtho
my solution gives perfect result in ideone.com but on spoj it says sigabrt !
am not getting it why !
Please help
<snip>

Last edit: 2023-06-02 23:42:12
2015-03-05 17:23:27 Anshuman Suri
Nice question :D
2015-02-18 19:47:44 Shubhankar mishra
use modulo wisely
2015-02-16 17:25:40 Daniel Carvalho
Bad question. Can't get AC in 1 trial without reading comments.
2015-02-10 07:59:00 Priyansh Saxena
How do I get rid of NZEC with Python 3.4.
Works fine with my interpreter.
2015-02-09 17:12:59 Dinesh
i think its large input! so careful on that
2015-02-08 05:43:30 Abhishek Naik
I understood that we need to use long long int after reading the comments. How could I have understood this without reading the comments? I prefer not to read them. Is there any clue in the problem that mentions this?
2015-02-02 11:27:51 Mercury
Good question to remember modulusr.

Last edit: 2015-02-02 11:28:04
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