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 modpow(long long a, long long n, long long mod) {
  if(a == 0 && n == 0) 
    return 1;
  long long res = 1;
  while (n > 0) {
    if (n & 1) res = res * a % mod;
    a = a * a % mod;
    n >>= 1;
  }
  return res;
}

int main(void){
  int N;
  scanf("%d", &N);
  int a[N];
  int c[100001]={};

  for(int i=0; i<N; i++){
    scanf("%d", &a[i]);
    c[a[i]]++;
  }

  long long ans = 1;
  
  if(c[0] != 1) {
    printf("0");
    return 0;
  }

  for(int i=0; i<100000; i++){
    if(c[i] == 0 && c[i+1] != 0){
      printf("0");
      return 0;
    }
  }

  for(int i=0; i<100000; i++){
    ans = (ans * modpow(c[i], c[i+1], 998244353)) % 998244353;
  }

  printf("%lld", ans); 
  return 0;
}