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>

long power(long a,long b){
  long i,n=1;
  if(a==0){
    return(0);
  }
  for(i=0;i<b;i++){
    n*=a;
  }
  return(n);
}

int main(){
  int n,i,a[100005],b;
  long m=1;
  for(i=0;i<100005;i++){
    a[i]=0;
  }
  scanf("%d",&n);
  for(i=0;i<n;i++){
    scanf("%d",&b);
    if((b==0)&(i!=0)){
      m=0;
      break;
    }
    a[b]++;
  }
  if((n==1)&(a[0]==0)){
    printf("1");
    return(0);
  }
  for(i=1;i<n;i++){
    if(a[i]==0){
      continue;
    }
    if(a[i-1]==0){
      m=0;
      break;
    }
    m*=power(a[i-1],a[i]);
  }
  printf("%d",m%998244353);
  return(0);
}