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
randomabraham: 2019-03-17 05:55:47

What are the limits on N and T?

s106062127: 2019-03-09 16:46:14

Limit should really be offered. We are solving problem, not playing guessing game.

souravramos04: 2019-02-14 16:47:51

Refer 1st part of this link i.e. Modular Arithmetic as Remainders, you'll get the idea : https://brilliant.org/wiki/modular-arithmetic/
Got AC on 11th attempt...totally worth it !

Last edit: 2019-02-14 16:56:59
abhinav_99: 2019-01-08 19:38:34

use modular division in every iteration otherwise WA

sanchit_aga: 2019-01-06 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 -

import sys
inp = [line for line in sys.stdin]

mukulsingh: 2019-01-04 19:14:24


Last edit: 2019-01-04 19:14:55
laidactienbn: 2018-11-04 16:33:04

For NZEC runtime error in python 3:
use input("\n") before the test case

midoriya: 2018-10-27 12:49:13

how should i take input cant figure it out please help i'm doing it in c++

anant6025: 2018-09-19 10:50:36

Just Google up the properties of the modulous function and code those which u think can be helpful for you in this problem.

I could have wrote that property here but than it will defeat the purpose of this problem.

probeta: 2018-08-30 16:09:21

Think over the fact that range for number of candies is not given , so it can be very very large :)


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