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)

//#include <bits/stdc++.h>
#include <iostream>
#include <vector>
#include <string>
using namespace std;
typedef long long ll;
const double EPS = 1e-9;
typedef vector<int> vint;
typedef pair<int, int> pint;
#define inf 1e+9
#define rep(i, n) REP(i, 0, n)
#define all(v) v.begin(), v.end()
#define msg(a) cout << #a << " " << a << endl;
#define REP(i, x, n) for(int i = x; i < n; i++)
#define pri(a) cout << a << endl;

int main(){
  cin.tie(nullptr);
	ios::sync_with_stdio(false);

  long long int n,ans=1;
  long long int c = 998244353;
  cin >> n;
  //ll n,k,ans=0;
  //cin >> n >> k;
  // string s;
  // cin >> s;

  vint v(n);
	rep(i,n){
		cin >> v[i];
	}

  //昇順
  //std::sort(v.begin(),v.end());

  if(v[0]!=0){
    cout << "0" << endl;
    return 0;
  }

  for(int i=1;i<n;i++){
    // if(v[i]==0){
    //   v[i] = 1;
    // }
    ans *= v[i];
  }

  pri(ans%c);

}