A12258. Array Without Local Maximums

Ivan unexpectedly saw a present from one of his previous birthdays. It is array of $n$ numbers from $1$ to $200$ . Array is old and some numbers are hard to read. Ivan remembers that for all elements at least one of its neighbours ls not less than it, more formally:

$a_{1} \le a_{2}$ ,

$a_{n} \le a_{n-1}$ and

$a_{i} \le max(a_{i-1}, \,\, a_{i+1})$ for all $i$ from $2$ to $n-1$ .

Ivan does not remember the array and asks to find the number of ways to restore it. Restored elements also should be integers from $1$ to $200$ . Since the number of ways can be big, print it modulo $998244353$ .

First line of input contains one integer $n$ ( $2 \le n \le 10^{5}$ ) — size of the array.

Second line of input contains $n$ integers $a_{i}$ — elements of array. Either $a_{i} = -1$ or $1 \le a_{i} \le 200$ . $a_{i} = -1$ means that $i$ -th element can't be read.

Print number of ways to restore the array modulo $998244353$ .

In the first example, only possible value of $a_{2}$ is $2$ .

In the second example, $a_{1} = a_{2}$ so there are $200$ different values because all restored elements should be integers between $1$ and $200$ .