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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<math.h>
long long fun(int val[],int c){
  if(c==0){
    if(val[c]==1)
      return 1;
    else return 0;
  }  
  else if(val[c]==0)
    return 0;

  else if(c==1&&val[0]==1)
    return 1;
  else if(c==1&&val[0]!=1)
    return 0;
  else
    return (pow( (fun(val,c-1)) * val[c-1],val[c] ));
}
int main(){
  int  n;
  scanf("%d",&n);
  int d[n];
  int val[n];
  for(int i=0;i<n;i++)
    val[i]=0;
  int mo;
  for(int i=0;i<n;i++){
    scanf("%d",&mo);
    d[i]=mo;
    val[mo]++;
  }
  int k;
 /* for(int i=0;i<n;i++){
    k=0;
    for(int j=0;j<n;j++){
      if(d[j]==i)
        k++;
    }
    val[i]=k;
  }*/
  //for(int i=0;i<n;i++)
    //printf("%d",val[i]);
  int m;
  for(int c=n-1;c>=0;c--){
    if(val[c]!=0){
      m=c;
      break;
    }
  }
  //printf("%d",m);
  printf("%ll",fun(val,m)%998244353);
  return 0;
}