Problem Description

There are $N$ numbers arranged in a row (representing heights). Initially, all numbers are zero. You can choose a continuous segment of numbers of the same height and increase them all by 1 (except for the first and last number in the segment). The following diagram illustrates two operations:

Now, some numbers are unclear and are represented by $-1$. You need to determine how many possible solutions exist such that the visible numbers exactly match the described operation method.

Input Format

The first line contains a positive integer $N$, representing the number of numbers.
The next line contains $N$ numbers, each representing the height of a number. $-1$ indicates an unclear number, which can be replaced by any number that satisfies the conditions. The $i$-th number is denoted by $h_i$.

Output Format

A single number representing the total number of possible solutions modulo $1000000007$.

Sample Input and Output

Sample Input #1

3
-1 2 -1

Sample Output #1

0

Sample Input #2

3
-1 -1 -1

Sample Output #2

2

Sample Input #3

6
-1 -1 -1 2 -1 -1

Sample Output #3

3

Notes

• $1 \leq N \leq 10000$
• $-1 \leq h_i \leq 10000$

见题面 Input 部分

见题面 Output 部分