No-Divisible Range

AtCoder

IDabc435_b

Time2000ms

Memory256MB

Difficulty—

You are given a sequence of positive integers $A=(A_1,A_2,\ldots,A_N)$ of length $N$. Find the number of pairs of integers $(l,r)$ satisfying $1\leq l\leq r\leq N$ that satisfy the following condition: > For every integer $i$ satisfying $l\leq i\leq r$, $A_i$ is **not** a divisor of $A_l+A_{l+1}+\cdots+A_r$. ## Constraints * $1 \leq N \leq 50$ * $1 \leq A_i \leq 1000$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5
8 6 10 5 7

Output #1

6

We have $A=(8,6,10,5,7)$.
For example, $(l,r)=(1,2)$ satisfies the condition because $A_l+A_{l+1}+\cdots+A_r=A_1+A_2=14$, and neither $A_1=8$ nor $A_2=6$ is a divisor of $14$.  
On the other hand, $(l,r)=(1,3)$ does not satisfy the condition because $A_l+A_{l+1}+\cdots+A_r=A_1+A_2+A_3=24$, and $A_1=8$ is a divisor of $24$.
The pairs that satisfy the condition are $(l,r)=(1,2), (1,4), (2,3), (2,4), (3,5), (4,5)$, which is six pairs, so output $6$.

Input #2

3
1 1 1

Output #2

API Response (JSON)

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