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 $B_1,B_2,…,B_k$ so that the following condition is satisfied:

• For every $i$( $1≤i≤k)$, 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:

$N$

$A_1$ $A_2$ .… $A_N$

Output

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

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Sample Input 1

4
1 2 3 4

Sample Output 1

3

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

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

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Sample Input 2

5
8 6 3 3 3

Sample Output 2

5

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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.

Constraints

• $1≤N≤3000$
• $1≤A_i≤10^{15}$
• For 5% test cases, $n \le 10$.
• For 20% test cases, $n \le 500$.
• For 50% test cases, $n \le 800$.
• For 100% test cases, $n \le 3000$.
• All values in input are integers.