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;

#define ll long long int
#define ull unsigned long long int
#define REPL(i,n) for(ll i=0, i##_len=(n); i<i##_len; ++i)
#define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)
#define radrad(a)  180.0 * a / M_PI
#define pow(x) x*x
static const int MAX = 100010;
static const ll INFTY = 1e12;
static const int NUMMAX = 300;


int main() {

  int N;
  ull ans = 1;
  ll tmp = 1;
  ll maxmax = 0;

  cin >> N;

  vector<int> num(MAX, 0);

  REP(i, N){
    cin >> tmp;
    num[tmp]++;
    maxmax = max(maxmax, tmp);
  }

  REPL(i, maxmax){
    if(num[i] == 0){
      ans = 0;
      break;
    }
    REP(j, num[i+1]){
      ans *= num[i];       
      if(ans > 998244353){
        ans %= 998244353;
      }
    }
    if(ans > 998244353){
      ans %= 998244353;
    }
  }


  cout << (ans % 998244353) << endl;


  return 0;

}
/*
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                   `=---='
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
         pass System Test!
*/