An array B of length M consisting of only distinct elements is said to be good if the following condition holds:
Let i be the index of the maximum element of B.
Then, B[1,i] must be in ascending order, $i.e, B_{1} < B_{2} < B_{3} < \ldots < B_{i}$.

For example, [1, 2, 3], [1, 4, 3, 2] and [1, 3, 2] are good arrays, while [2, 1, 3] and [3, 2, 4, 1] are not.

You are given a permutation P of length N. You have to partition P into some non-empty good [subarrays]. Note that every element of P should be contained in exactly one subarray.

Find the total number of valid partitions.

Since the answer can be quite large, please print it modulo 998244353.

Note: A permutation of length N is an arrangement of the integers ${1, 2, 3, \ldots, N$}.

------ Input Format ------

• The first line of input contains a single integer T denoting the number of test cases. The description of T test cases follows.
• Each test case consists of two lines of input.
• The first line of each test case contains a single integer N, the length of P.
• The second line contains $N space-separated distinct integers P_{1}, P_{2}, P_{3} , \ldots, P_{N}$.

------ Output Format ------

For each test case, output on a new line the number of valid partitions modulo 998244353.

------ Constraints ------

$1 ≤ T ≤ 10^{5}$
$1 ≤ N ≤ 10^{6}$
$1 ≤ P_{i} ≤ N$ for each $1 ≤ i ≤ N$.
- All elements of $P$ are distinct.
- The sum of $N$ over all test cases won't exceed $10^{6}$.

----- Sample Input 1 ------
2
4
2 1 4 3
5
1 2 3 4 5

----- Sample Output 1 ------
6
16

----- explanation 1 ------
Test case $1$: The $6$ valid partitions are as follows:
- $[2], [1], [4], [3]$
- $[2], [1], [4, 3]$
- $[2], [1, 4], [3]$
- $[2], [1, 4, 3]$
- $[2, 1], [4], [3]$
- $[2, 1], [4, 3]$

见题面

见题面