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 <iostream>
#include <cstdio>
#include <algorithm>
#include <cmath>

using namespace std;
typedef long long ll;
ll last,a,b,c,i,j,k,m,n,str[100005],sum=1;
int main()
{
    scanf("%lld",&n);
    for(i=0;i<n;i++){
        scanf("%lld",&str[i]);
    }
    sort(str,str+n);
    j=0;
    for(i=0;i<n;i++){
        if(str[i]==j)
            j++;
        else if(str[i]>j)
            break;
    }
    if(i!=n)
        {printf("0\n");return 0;}

    j=0;
    while(str[j]==0)
    {
        j++;
    }
    last=j;
        j=1;
        b=0;
        for(i=1;i<n;i++){
            if(str[i]==j)
            {
                sum=sum*last%998244353;
                b++;
            }
            else if(str[i]!=0)
            {
                j=str[i];
                last=b;
                sum=sum*last%998244353;
                b=1;
            }
        }
        if(i==n)
        {
            printf("%lld\n",sum);
        }
    return 0;
}