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>
#define rep(i, n) for (int i=0;i<(n);i++)
#define ll long long
using namespace std;

const ll mod=998244353;

ll pow(int a, int b) {
  ll x=1;
  rep(i, b) {
    x*=a;
    x%=mod;
  }
  return x;
}

int main() {
  int n;
  cin>>n;
  vector<int> d(n-1);
  int maxd=0;
  rep(i, n) {
    int x;
    cin>>x;
    d[x]++;
    maxd=max(maxd, x);
  }
  ll ans=1;
  rep(i, maxd+1) {
    if (d[i]==0) {
      ans=0;
      break;
    }
    ans*=pow(d[i], d[i+1]);
    ans%=mod;
  }
  cout<<ans<<endl;
}