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 long poworg(long long a, long long b){
  long long ans=1;
  for(long long i=0;i<b;i++){
    ans *= a;
  }
  return ans;
}
int main() {
  long long N,i;
  scanf("%lld", &N);
  long long D[N], countD[N];
  for(i=0;i<N;i++){
    countD[i] = 0;
  }
  for(i=0;i<N;i++){
    scanf("%lld",&D[i]);
    countD[D[i]]++;
  }

  if(countD[0]!=1){
    printf("0\n");
    return 0;
  }
  for(i=1;i<N;i++){
    if(countD[i]!=0 && countD[i-1]==0){
      printf("0\n");
      return 0;
    }
  }
  
  long long ans=1;
  for(i=1;i<N;i++){
    ans *= poworg(countD[i-1],countD[i]);
  }
  printf("%lld\n",ans%998244353);
  
  return 0;
}