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).

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).

Constraints

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

Sample Input 1

4
1 2 3 4

Sample Output 1

3

We have three ways to separate the sequence, as follows:

• (1),(2),(3),(4)
• (1,2,3),(4)
• (1,2,3,4)

Sample Input 2

5
8 6 3 3 3

Sample Output 2

5

Sample Input 3

10
791754273866483 706434917156797 714489398264550 918142301070506 559125109706263 694445720452148 648739025948445 869006293795825 718343486637033 934236559762733

Sample Output 3

15

The values in input may not fit into a 32-bit integer type.

见题面 Input 部分

见题面 Output 部分