Problem Statement

Solve the following problem for $T$ test cases.

Given an integer $N$ and a string $S$, find the number of strings $X$ that satisfy all of the conditions below, modulo $998244353$.

• $X$ is a string of length $N$ consisting of uppercase English letters.
• $X$ is a palindrome.
• $X \\le S$ in lexicographical order.
  • That is, $X=S$ or $X$ is lexicographically smaller than $S$.

Constraints

• $1 \\le T \\le 250000$
• $N$ is an integer between $1$ and $10^6$ (inclusive).
• In a single input, the sum of $N$ over the test cases is at most $10^6$.
• $S$ is a string of length $N$ consisting of uppercase English letters.

Input

Input is given from Standard Input in the following format:

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

Here, $\\mathrm{case}_i$ represents the $i$-th test case.

Each test case is in the following format:

$N$ $S$

Output

Print $T$ lines. The $i$-th line should contain the answer for the $i$-th test case as an integer.

Sample Input 1

5
3
AXA
6
ABCZAZ
30
QWERTYUIOPASDFGHJKLZXCVBNMQWER
28
JVIISNEOXHSNEAAENSHXOENSIIVJ
31
KVOHEEMSOZZASHENDIGOJRTJVMVSDWW

Sample Output 1

24
29
212370247
36523399
231364016

This input contains five test cases.

Test case #1:
The $24$ strings satisfying the conditions are AAA$,$ ABA$,$ ACA$,...,$ AXA.

Test case #2:
$S$ may not be a palindrome.

Test case #3:
Be sure to find the count modulo $998244353$.