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;
long long int mod = 998244353;

int main() { 
  long long int n, d_, p, ans = 1;
  cin >> n;
  map<long long int, long long int> d;
  for(int i = 0; i < n; ++i) {
    cin >> d_;
    d[d_]++;
  }
  // ここまではOK

  auto begin = d.begin(), end = d.end();
  if(begin->first != 0) {
    // これは正しい
    cout << 0 << '\n';
    return 0;
  } else if(begin->second != 1) {
    // これも正しい
    cout << 0 << '\n';
    return 0;
  }

  for(auto iter = begin; iter != next(end, -1); iter++) {
    if(iter->first != (next(iter, 1)->first)-1) {
      // 多分ちゃんと動いてくれてる
      cout << 0 << '\n';
      return 0;
    }
    p = 1;
    for(long long int i = 0; i < next(iter, 1)->second; ++i) {
      p *= iter->second;
      p %= mod;
    }
    ans *= p;
    ans %= mod;
    /* オーバーフローもmod取り忘れもない、でも2つのWAが取れない
    * 2つだから多分終了条件の見逃しだと思う
    */
  }
  cout << ans%mod << '\n';
}