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 <iostream>
#include <string>
#include <unordered_map>
#include <stdio.h>
#include <list>
#include <vector>
#include <algorithm>
#include <stack>
#include <climits>
#include <queue>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; ++i)
typedef long long ll;

int main()
{
	ll n;
	cin >> n;
	vector<ll> D(n);
	rep(i,n)D[i]=0;
	rep(i,n)
	{
		ll foo;cin>>foo;
		D[foo] ++;
	}

	ll ans=1;
	bool zero=false;

	for(ll i = 1;i<n;i++)
	{
		if(D[i]==0)
		{
			zero=true;
			for(i;i<n;i++)
			{
				if(D[i]>0)
				{
					cout<<0<<endl;
					return 0;
				}
			}
		}

	if(!zero)
		rep(jj,D[i])
		{
			ans*=D[i-1];
			ans%=998244353;
		}

	}
	cout<<ans<<endl;

	return 0;
}