Problem:
Score : 300 points

Problem Statement

Given is an integer sequence D_1,...,D_N of N elements. Find the number, modulo 998244353, of trees with N vertices numbered 1 to N that satisfy the following condition:

For every integer i from 1 to N, the distance between Vertex 1 and Vertex i is D_i.

Notes

A tree of N vertices is a connected undirected graph with N vertices and N-1 edges, and the distance between two vertices are the number of edges in the shortest path between them.

Two trees are considered different if and only if there are two vertices x and y such that there is an edge between x and y in one of those trees and not in the other.

Constraints

1 \leq N \leq 10^5

0 \leq D_i \leq N-1

Input

Input is given from Standard Input in the following format:

N
D_1 D_2 ... D_N

Output

Print the answer.

Sample Input 1

4
0 1 1 2

Sample Output 1

2

For example, a tree with edges (1,2), (1,3), and (2,4) satisfies the condition.

Sample Input 2

4
1 1 1 1

Sample Output 2

0

Sample Input 3

7
0 3 2 1 2 2 1

Sample Output 3

24

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
const int MAX = 1e5+7;
typedef long long ll;
const ll mod=998244353;
ll d[MAX];
ll quick(ll a,ll b){
    ll res=1;
    while(b){
        if(b&1) res=res*a%mod;
        a=a*a%mod;
        b>>=1;
    }
    return res;
}
int main(){
    int n;
    while(~scanf("%d", &n)){
        memset(d,0,sizeof(d));
        int pos=0,val;
        for(int i=0;i<n;i++){
            //int val;
            scanf("%d", &val);
            d[val]++;
            pos=max(pos,val);
        }
        int flag=1;
        ll ans=1,cnt=1;
        for(int i=0;i<=pos;i++){
            if(d[i]==0 || d[0]!=1){
                flag=0;
                printf("%d\n", 0);
                break;
            }
            ans=ans*quick(cnt,d[i])%mod;
            cnt=d[i];
        }
        if(flag) printf("%lld\n", ans);
    }
    return 0;
}