![](data:image/png;base64,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)
화학 연구실의 연구원인 홍현이는 미리 준비해놓은
개의 화학 약품을 가지고 이를 조합하여 새로운 화합물을 만들어내고자 한다. 화학 약품은 어떤 약품끼리 섞이느냐에 따라 매우 다른 반응을 보이며, 때에 따라 매우 위험한 결과물이 나올 수 있어 다음과 같은 방법을 이용해 약품을 섞고자 한다.
- 주어진 화학 약품에는 고유값
가 있다. - 화합물
를 만들고자 할 때, 들어가는 화학 약품의 고유값의 합이 0이 되도록 만든다.
화학 약품의 고유값이 주어졌을 때 홍현이가 만들 수 있는 화합물의 개수를 구해보자.
입력
첫 번째 줄에는 화학 약품의 개수
이 주어진다. ![](/texconverter?eq=(1%20%5Cleq%20N%20%5Cleq%2040))
두 번째 줄에는 화학 약품의 고유값
가 공백으로 구분되어 주어진다. ![](/texconverter?eq=(-1%2C000%2C000%20%5Cleq%20a_i%20%5Cleq%201%2C000%2C000%20%20%5C%20%5C%20%5C%20a_i%20%5Cneq%200))
출력
홍현이가 만들 수 있는 화합물의 개수를 출력한다.