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>
using namespace std;
using vi = vector<int64_t>;

const int64_t C = 998244353;

int64_t power(int64_t x, int64_t y){
  int64_t ans = 1;
  for(int64_t i=0; i<y; i++){
    ans = (ans * x) % C;
  }
  return ans;
}

int main(){
  int N;
  vi count(100010); //count[i] = 距離iの点の個数

  cin >> N; int maximum = 0;
  for(int i=0; i<N; i++){
    int tmp; cin >> tmp;

    if(i==0 && tmp == 1){
      cout << 0 << endl;
      return 0;
    }

    count[tmp]++;
    maximum = max(maximum,tmp);
  }

  int64_t ans = 1;
  for (int i=1; i<=maximum; i++){
    ans = (ans * power(count[i-1], count[i])) % C;
  }

  cout << ans << endl;;
}