1349_D. Slime and Biscuits
Slime 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 + … + 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 p/q for coprime p and q, you need to find the value of (p ⋅ q^{-1})mod 998 244 353. You can prove that qmod 998 244 353 ≠ 0.

Input

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

The second line contains n non-negative integers a_1,a_2,...,a_n\ (1≤ a_1+a_2+...+a_n≤ 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 1/2, and the probability that player 2 will give the player 1 a biscuit is 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.
```python
import os
import sys
input = sys.stdin.buffer.readline
#sys.setrecursionlimit(int(2e5)) 
from collections import deque
import math
#  list(map(int, input().split()))
#####################################################################################

class CF(object):
    def __init__(self):
        self.mod = 998244353
        self.n = int(input())
        self.a = list(map(int, input().split()))
        self.tot = sum(self.a)
        self.dp = [[0,0] for _ in range(self.tot+1)]

    def inv(self, x):
        return pow(x, self.mod - 2, self.mod)

    def gao(self):
        self.dp[0] = [0,1]
        self.dp[1] = [(1-self.n+self.mod)%self.mod, 1]
        for k in range(1, self.tot):
            temp = self.inv(self.tot-k)
            self.dp[k+1][0] = -self.tot*(self.n - 1) - self.dp[k][0] * (2*k - self.tot- k*self.n) - self.dp[k-1][0] *k*(self.n-1)
            self.dp[k+1][0] *= temp
            self.dp[k+1][0] = (self.dp[k+1][0] %self.mod+self.mod)%self.mod            
            self.dp[k+1][1] = -self.dp[k][1]*(2*k - self.tot- k*self.n) - self.dp[k-1][1]*k*(self.n-1)
            self.dp[k+1][1] *= temp
            self.dp[k+1][1] = (self.dp[k+1][1] %self.mod+self.mod)%self.mod
        
        alpha = -self.dp[self.tot][0]*self.inv(self.dp[self.tot][1])
        alpha = (alpha%self.mod + self.mod)%self.mod
        #print(alpha)
        ans=0
        for i in range(self.n):
            ans += self.dp[self.a[i]][0] + self.dp[self.a[i]][1] * alpha
            ans = (ans%self.mod+self.mod)%self.mod
        ans -= alpha * (self.n - 1)
        ans = (ans%self.mod+self.mod)%self.mod
        ans *= self.inv(self.n)
        ans = (ans%self.mod+self.mod)%self.mod
        print(ans)


    def main(self):            
        self.gao()
        pass

if __name__ == "__main__":
    cf = CF()
    cf.main()
    pass

'''
dp[k+1] *(tot-k) = -tot*(n-1) - dp[k]*(2*k - tot- k*n ) - dp[k-1] *k*(n-1)

'''
```