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;
typedef long long ll;
typedef unsigned long long ull;
#define pb push_back
#define fi first
#define se second
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define pre(i,a,b) for(int i=(a);i>(b);i--)
const int maxn=1e5+10;
const int mod=998244353;
const int inf=0x3f3f3f3f;
int book[maxn];
int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);
	int n;
	cin>>n;
	rep(i,0,n)
	{
		int x;
		cin>>x;
		book[x]++;
	}
	ll ans=1;
	rep(i,1,n)
	{	
		if(book[i]==0) continue;
		if(book[i-1]==0) ans=0;
		else 
		{
			rep(j,0,book[i]) ans=ans*book[i-1]%mod;
		}
	}
	cout<<ans<<'\n';
    return 0;
}