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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

// Bismillahirrahmanirrahim
#include<bits/stdc++.h>
using namespace std;


#define mod 998244353

long long power(long long base,long long pow) {
  long long res = 1;
  for(int i = 0; i < pow; i++) res = (res* base) % mod;
  return res;
}

long long arr[(int)1e5+5];
int main() {
  int n;cin >> n;
  for(int i = 0; i < n;i++) {
    int x; cin >> x;arr[x]++;
  }
  if(arr[0] != 1) {cout << 0 <<endl; return 0;}
  long long res = 1;
  for(int i = 2; i <= n;i++) {
    res = res * (power(arr[i-1],arr[i]))%mod;
  }
  cout << res << endl;
}