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<stdlib.h>
#include<math.h>
int compare_int(const void *a,const void *b){
  return *(int *)a-*(int *)b;
}
int main(void)
{
  int n,cnt=0,j=0,before=0;
  long long ans=1;
  scanf("%d",&n);
  int d[n];
  for(int i=0;i<n;i++){
    scanf("%d",&d[i]);
  }
  if(d[0]!=0){
    puts("0");
    return 0;
  }
  qsort(d,n,sizeof(int),compare_int);
  int val[d[n-1]+1];//d[i]の最大値個のサイズ+1
  if(d[1]==0){
    puts("0");//
    return 0;
  }

  while(1){
    if(d[j]==d[j+1]){
      cnt++;
    }else if(d[j]+1==d[j+1]){
      val[d[j]]=cnt;
      cnt=1;
    }else{
      puts("0");
      return 0;
    }
    j++;
    if(j==n-1){
      break;
    }
  }
  val[d[n-1]]=cnt;
  //printf("valdn-1=%d\n",d[n-1]);

  for(int i=d[n-1];i>1;i--){
    ans*=pow(val[i-1],val[i]);
    //printf("i=%d ans=%lld\n",i,ans);
    //ans*=val[d[i]]*val[d[i]-1];
    //ans*=d[i]*val[d[i]-1];
  }
  ans=ans%998244353;
  /*
  for(int i=0;i<d[n-1]+1;i++){
    printf("val[%d]=%d",i,val[i]);
  }*/
  printf("%lld",ans);
  return 0;
}