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<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
typedef long long ll;
const int N=1e5+4;
const int MOD=998244353;
int n,d[N];
int cnt[N],tot;
int fpow(int a,int b,int m) {
	int ret=1;
	while (b) {
		if (b&1) ret=1ll*ret*a%m;
		b>>=1,a=1ll*a*a%m;
	}
	return ret;
}
int main() {
	scanf("%d",&n);
	for (register int i=1;i<=n;++i) {
		scanf("%d",&d[i]);
		tot=max(tot,d[i]);
		++cnt[d[i]];
	}
	bool f=true;
	for (int i=0;i<=tot;++i)
		if (!cnt[i]) {
			f=false;
			break;
		}
	if (!f||cnt[0]>1) {
		puts("-1");
		return 0;
	}
	int ans=1;
	for (int i=1;i<=tot;++i) {
		int x=cnt[i-1],y=cnt[i];
		ans=1ll*ans*fpow(x,y,MOD)%MOD;
	}
	printf("%d\n",ans);
	return 0;
}