시간 제한메모리 제한제출정답맞힌 사람정답 비율
1 초 1024 MB77118515834.423%

문제

길이가 $N$인 수열 $A_1, \cdots, A_N$이 주어집니다. 아래 조건을 모두 만족시키는 $(i, j)$ 정수쌍의 개수를 구하세요.

  • $1 \le i \le j \le N$
  • $A_i + A_{i+1} + \cdots + A_j = A_i \times A_{i+1} \times \cdots \times A_j$

입력

첫 줄에 수열의 길이 $N$이 주어집니다. $(1 \le N \le 300\,000)$

둘째 줄에 $N$개의 정수 $A_1, \cdots, A_N$ 이 공백으로 구분되어 주어집니다. $(1 \le A_i \le 300\,000)$

출력

문제의 조건을 만족시키는 $(i, j)$ 정수쌍의 개수를 출력하세요.

예제 입력 1

6
3 1 2 4 1 5

예제 출력 1

8

문제의 조건을 만족하는 $(i, j)$ 정수쌍과 이에 해당하는 $[A_i, \cdots, A_j]$는 다음과 같습니다.

  • $(1, 1)$: $[3]$
  • $(1, 3)$: $[3, 1, 2]$
  • $(2, 2)$: $[1]$
  • $(2, 5)$: $[1, 2, 4, 1]$
  • $(3, 3)$: $[2]$
  • $(4, 4)$: $[4]$
  • $(5, 5)$: $[1]$
  • $(6, 6)$: $[5]$
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