시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 128 MB62462204194738.878%

문제

사탕 박사 고창영은 사탕 공장을 그만 두고 초등학교 선생님으로 취직했다.

오늘은 창영이네 반 학생들과 소풍을 가는 날이다. N명의 학생은 모두 가방에 사탕을 가득 담아왔다.

그런데, 사탕을 많이 가져온 학생들이 사탕을 적게 가져온 학생들을 놀리기 시작했다.

창영이는 "얘들아~ 그러면 안되지ㅜㅜ 사탕을 모두 여기에 가져와보렴. 선생님이 공평하게 나눠줄게"

창영이는 모든 학생들이 같은 사탕을 가지게 하려고 한다.

이것이 가능한 일일까?

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스는 빈 줄로 구분되어 있고, 다음과 같이 구성되어 있다.

테스트 케이스의 첫째 줄에 학생의 수 N이 주어진다. 다음 N개의 줄에는 각 학생들이 가져온 사탕의 수가 주어진다.

N은 100,000보다 작거나 같은 자연수이고, 사탕의 개수는 0보다 크거나 같은 정수이다. 학생들이 가져온 사탕 개수는 1018보다 작거나 같다. (학생들이 가져온 사탕 개수의 합은 1018을 넘어갈 수 있다)

출력

각 테스트 케이스에 대해 모두에게 같은 사탕을 나눠줄 수 있으면 YES를, 없으면 NO를 출력한다.

예제 입력 1

2

5
5
2
7
3
8

6
7
11
2
7
3
4

예제 출력 1

YES
NO
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