Problem Statement

Given is a sequence $A$ of $N$ numbers. Find the number of ways to separate $A$ into some number of non-empty contiguous subsequence $B_1, B_2, \ldots, B_k$ so that the following condition is satisfied:

• For every $i\ (1 \leq i \leq k)$, the sum of elements in $B_i$ is divisible by $i$.

Since the count can be enormous, print it modulo $(10^9+7)$.

Constraints

• $1 \leq N \leq 3000$
• $1 \leq A_i \leq 10^{15}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 \ldots A_N

Output

Print the number of ways to separate the sequence so that the condition in the Problem Statement is satisfied, modulo $(10^9+7)$.