Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
D. Slime and Biscuits

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSlime and his $$$n$$$ friends are at a party. Slime has designed a game for his friends to play.

At the beginning of the game, the $$$i$$$-th player has $$$a_i$$$ biscuits. At each second, Slime will choose a biscuit randomly uniformly among all $$$a_1 + a_2 + \ldots + a_n$$$ biscuits, and the owner of this biscuit will give it to a random uniform player among $$$n-1$$$ players except himself. The game stops when one person will have all the biscuits.

As the host of the party, Slime wants to know the expected value of the time that the game will last, to hold the next activity on time.

For convenience, as the answer can be represented as a rational number $$$\frac{p}{q}$$$ for coprime $$$p$$$ and $$$q$$$, you need to find the value of $$$(p \cdot q^{-1})\mod 998\,244\,353$$$. You can prove that $$$q\mod 998\,244\,353 \neq 0$$$.

Input

The first line contains one integer $$$n\ (2\le n\le 100\,000)$$$: the number of people playing the game.

The second line contains $$$n$$$ non-negative integers $$$a_1,a_2,\dots,a_n\ (1\le a_1+a_2+\dots+a_n\le 300\,000)$$$, where $$$a_i$$$ represents the number of biscuits the $$$i$$$-th person own at the beginning.

Output

Print one integer: the expected value of the time that the game will last, modulo $$$998\,244\,353$$$.

Examples

Input

2 1 1

Output

1

Input

2 1 2

Output

3

Input

5 0 0 0 0 35

Output

0

Input

5 8 4 2 0 1

Output

801604029

Note

For the first example, in the first second, the probability that player $$$1$$$ will give the player $$$2$$$ a biscuit is $$$\frac{1}{2}$$$, and the probability that player $$$2$$$ will give the player $$$1$$$ a biscuit is $$$\frac{1}{2}$$$. But anyway, the game will stop after exactly $$$1$$$ second because only one player will occupy all biscuits after $$$1$$$ second, so the answer is $$$1$$$.

Codeforces (c) Copyright 2010-2022 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/21/2022 01:57:34 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|