Problem Description

Xiao Lan developed a game called “Lanqiao Monopoly”. There are a total of $2026$ players in the game, numbered from $1$ to $2026$.

At the start of the game, each player has some initial points. In particular, player $i$ starts with $i$ points.

The game goes through multiple rounds of point updates. In each round, all players’ points are updated at the same time: for any player, their new points equal the product of the points of all other players except themselves, before this round’s update. For example, with $3$ players whose initial points are $1, 2, 3$, in the first round:

• Player $1$’s new points are $2 \times 3 = 6$.
• Player $2$’s new points are $1 \times 3 = 3$.
• Player $3$’s new points are $1 \times 2 = 2$.

So after the first round ends, the three players’ points become $6, 3, 2$.

Now, please compute the value of the total product of points of all $2026$ players after the $2026$-th round ends, modulo $998244353$.

Output Format

This is an output-only (fill-in-the-blank) problem. You only need to compute the result and submit it. The result is a single integer. When submitting, you only need to write a program that outputs this integer; any extra content will not receive any points.

Hint

Translated by ChatGPT 5