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>
#define LL long long
#define maxn   100005
#define modn   998244353
using namespace std;
LL a[maxn];
LL quickpow(LL a,LL b)
{
    LL ans=1;
    a%=modn;
    while(b)
    {
        if(b%2==1)
          ans=(ans*a)%modn;
       a=(a*a)%modn;
       b/=2;
    }
    return ans;
}
int main()
{
    LL n;
    cin>>n;
    memset(a,0,sizeof(a));
    LL flag=0;
    LL maxroad=0;
    for(int i=0;i<n;i++)
    {
        LL k;
        scanf("%lld",&k);
        if(k<n)
            {
               a[k]++;
               maxroad=max(maxroad,k);
            }
        else
            flag=1;
    }
    LL ans=1;
    if(a[0]==0)
        flag=1;
    if(flag)
        ;
    else
    {
        for(int i=1; i<=maxroad; i++)
        {
            ans*=quickpow(a[i-1],a[i]);
            ans%=modn;
        }
    }
    if(flag)
        cout<<"0"<<endl;
    else
        cout<<ans<<endl;
}