Problem Statement

You are given an integer sequence $A=(A_1,A_2,\cdots,A_N)$ of length N.
You will perform the following operation exactly once:

• Choose a non-empty subsequence of A (not necessarily contiguous) and replace it with its cumulative sums.
  More precisely, first choose a sequence of indices $(i_1,i_2,\cdots,i_k)$ such that $1 \leq i_1 < i_2 < \cdots < i_k \leq N$.
  The length of the sequence $k (1 \leq k \leq N)$ can be chosen freely.
  Then, for each $j (1 \leq j \leq k),$ replace the value of A_{i_j} with $\sum_{1 \leq x \leq j} A_{i_x}$.
  This replacement is done simultaneously for all chosen indices.

Find, modulo 10^9+7, the number of possible sequences A after the operation.

Input

The input is given from Standard Input in the following format:
N
$A_1 A_2 \cdots A_N$

Output

Print the answer.

Constraints

• $1 \leq N \leq 100$
• -$10 \leq A_i \leq 10$
• All input values are integers.

Sample Input 1

3
1 1 2

Sample Output 1

4

The possible sequences A after the operation are as follows:

• A=(1,1,2): This can be achieved with k=1 and (i_1)=(1).
• A=(1,2,2): This can be achieved with k=2 and (i_1,i_2)=(1,2).
• A=(1,1,3): This can be achieved with k=2 and (i_1,i_2)=(1,3).
• A=(1,2,4): This can be achieved with k=3 and (i_1,i_2,i_3)=(1,2,3).

Sample Input 2

4
1 -1 1 -1

Sample Output 2

8

Sample Input 3

5
0 0 0 0 0

Sample Output 3

1

Sample Input 4

40
2 -2 1 3 -3 -1 -2 -3 0 -1 -2 0 -3 0 0 2 0 -1 2 -2 -2 -1 3 -2 -2 -2 2 3 2 -3 0 -2 2 1 3 0 -1 0 -2 -3

Sample Output 4

420429545

见题面 Input 部分

见题面 Output 部分