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>
#define mod 998244353
#define ll long long
using namespace std;
int main()
{
	ll n,a[1000000],flag=0;
	while(cin>>n)
	{
	for(int i=1;i<=n;i++)
		cin>>a[i];
		if(a[1]!=0)
		{
			cout<<"0";
			continue;
		}
		for(int i=2;i<=n;i++)
		{
			if(abs(a[i]-a[i-1]>1))
			{
				cout<<"0";
				continue;
			}
		}
		ll i=2,ans=1,t=0;
		for(;a[i]==1;i++)
			t++;
		for(;i<=n;)
		{
			ll d=a[i],s=1,num=0;
			for(;a[i]==d&&i<=n;i++)
			{
				num++;
				s = (s*t)%mod;
			}
			ans=(ans*s)%mod;
			t=num;
		}
		cout<<ans;
	}
	return 0;
}