You are given an array $$A$$ of $$N$$ integers. Now, some of the elements are missing from this array. It is known that the missing elements are integers that are less than or equal to the average of the numbers after and before that. Also, it is assured that if the number is missing then its neighbour elements will be present in the array. Your task is to count how many possible distinct arrays can be formed if the missing elements are restored. As the answer could be very large output it modulo $$10^9 + 7$$.

Note: If $$A[i] = -1$$ then it means that the number is missing. Also, the missing elements will always be in the index range $$2$$ to $$N - 1$$.

Input Format
The first line contains an integer $$N$$ that denote the total elements in the array $$A$$.
The next line contains $$N$$ space-separated integers that denote the elements of the array $$A$$.

Output Format
In the output, you need to print the total number of possible distinct arrays that can be formed after the array $$A$$ is restored.

Constraints
$$3 \le N \le 10^5$$
$$1 \le A[i] \le 10^5$$