[Solution] Everything Everywhere All But One Codeforces Solution | Codeforces Problem Solution 2022

[Solution] Everything Everywhere All But One Codeforces Solution | Codeforces Problem Solution 2022

A. Everything Everywhere All But One

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

You are given an array of n$n$ integers a1,a2,…,an$a_1,a_2,\dots ,a_n$. After you watched the amazing film "Everything Everywhere All At Once", you came up with the following operation.

In one operation, you choose n−1$n-1$ elements of the array and replace each of them with their arithmetic mean (which doesn't have to be an integer). For example, from the array [1,2,3,1]$[1,2,3,1]$ we can get the array [2,2,2,1]$[2,2,2,1]$, if we choose the first three elements, or we can get the array [43,43,3,43]$[\frac{4}{3},\frac{4}{3},3,\frac{4}{3}]$, if we choose all elements except the third.

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Is it possible to make all elements of the array equal by performing a finite number of such operations?

Input

The first line of the input contains a single integer t$t$ (1≤t≤200$1\le t\le 200$)  — the number of test cases. The description of the test cases follows.

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The first line of each test case contains a single integer n$n$ (3≤n≤50$3\le n\le 50$)  — the number of integers.
The second line of each test case contains n$n$ integers a1,a2,…,an$a_1,a_2,\dots ,a_n$ (0≤ai≤100$0\le a_i\le 100$).

Output

For each test case, if it is possible to make all elements equal after some number of operations, output YES$\mathtt{\text{YES}}$. Otherwise, output NO$\mathtt{\text{NO}}$.

You can output YES$\mathtt{\text{YES}}$ and NO$\mathtt{\text{NO}}$ in any case (for example, strings yEs$\mathtt{\text{yEs}}$, yes$\mathtt{\text{yes}}$, Yes$\mathtt{\text{Yes}}$ will be recognized as a positive response).