# 2874. Generic Cow Protests


























Farmer John's N (1 <= N <= 100,000) cows are lined up in a row and

numbered 1..N. The cows are conducting another one of their strange

protests, so each cow i is holding up a sign with an integer A_i

(-10,000 <= A_i <= 10,000).

FJ knows the mob of cows will behave if they are properly grouped

and thus would like to arrange the cows into one or more contiguous

groups so that every cow is in exactly one group and that every

group has a nonnegative sum.

Help him count the number of ways he can do this, modulo 1,000,000,009.

By way of example, if N = 4 and the cows' signs are 2, 3, -3, and

1, then the following are the only four valid ways of arranging the

cows:

(2 3 -3 1)

(2 3 -3) (1)

(2) (3 -3 1)

(2) (3 -3) (1)

Note that this example demonstrates the rule for counting different

orders of the arrangements.

### 输入格式
































* Line 1: A single integer: N

* Lines 2..N + 1: Line i + 1 contains a single integer: A_i



### 输出格式





























* Line 1: A single integer, the number of arrangements modulo

1,000,000,009.

### 样例

Input
4
2
3
-3
1

Output
4


2 人解决，3 人已尝试。

2 份提交通过，共有 10 份提交。

8.9 EMB 奖励。