Problem Statement

You are given a sequence of positive integers $A = (A_1, A_2, \cdots, A_N)$ of length $N$. Here, $A_1 \leq A_2 \leq \cdots \leq A_N$ holds.

Find the number, modulo $998\,244\,353$, of possible sequences of positive integers $B$ of length $N$ satisfying the following conditions.

• $1 \leq B_i \leq A_i$ ($1 \leq i \leq N$)
• The inversion number of $B$ is odd.

Here, the inversion number of $B$ is the number of pairs of integers $(i, j)$ satisfying $1 \leq i < j \leq N$ such that $B_i > B_j$.

Solve $T$ test cases per input file.

Constraints

• $1 \leq T \leq 10\,000$
• $1 \leq N \leq 200\,000$
• $1 \leq A_1 \leq A_2 \leq \cdots \leq A_N \leq 10^9$
• The sum of $N$ over the $T$ test cases is at most $400\,000$.
• All input values are integers.

Input

The input is given from Standard Input in the following format. Here, $\mathrm{case}_i$ ($1 \leq i \leq T$) denotes the $i$-th test case.

T
\mathrm{case}_1
\mathrm{case}_2
\vdots
\mathrm{case}_T

Each test case is given in the following format:

N
A_1 A_2 \cdots A_N

Output

Output $T$ lines. The $i$-th line ($1 \leq i \leq T$) should contain the answer for $\mathrm{case}_i$.