Note the unusual memory limit.

Consider the following pseudocode that processes a permutation $p$ of length $n$$^{\text{∗}}$:

function mystery(p):
    n = length of p
    st = an empty stack
    count = an array of length n filled with 0s
    for i from 1 to n:
        while st is not empty and p[i] < top of st:
            pop from st
            count[i] = count[i] + 1
        push p[i] into st
    return count

You are given an array $a$ of length $n$. Your task is to count the number of permutations $p$ of length $n$ such that, if $b$ is the array returned by mystery(p), the condition $a_i = b_i$ holds for all $i$ ($1 \le i \le n$) where $a_i \neq -1$.

Since the answer can be very large, output it modulo $998\,244\,353$.

$^{\text{∗}}$A permutation of length $n$ is an array consisting of $n$ distinct integers from $1$ to $n$ in arbitrary order. For example, $[2,3,1,5,4]$ is a permutation, but $[1,2,2]$ is not a permutation ($2$ appears twice in the array), and $[1,3,4]$ is also not a permutation ($n=3$ but there is $4$ in the array).

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 10^4$). The description of the test cases follows.

The first line of each test case contains an integer $n$ ($1 \le n \le 500$), representing the length of $a$.

The second line contains $n$ integers $a_1,a_2,\ldots,a_n$ ($-1 \le a_i \le n$), representing the elements in $a$.

It is guaranteed that the sum of $n^3$ over all test cases does not exceed $500^3$.

Output

For each test case, output an integer representing the number of permutations, modulo $998\,244\,353$.

Note

In the first and second test cases, the only valid permutation is $[1]$.

In the fourth test case, the valid permutations are $[1,2,4,3]$, $[3,4,2,1]$, and $[1,4,3,2]$.

In the fifth test case, all permutations of length $6$ are valid.