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 <iostream>
#define maxn 100005
using namespace std;
int n,d[maxn],num[maxn];
const int mod = 998244353;
long long ans=1;
long long my_pow(int x,int y){
    long long tmp=1;
    for(int i=1;i<=y;++i)
        tmp = (tmp*x)%mod;
    return tmp;
}
int main(){
    scanf("%d",&n);
    for(int i=1;i<=n;++i){
        scanf("%d",&d[i]);
        ++num[d[i]];
    }
    if(num[0]!=1){
        printf("0");
        return 0;
    }
    for(int i=1;i<n;++i){
        ans = (ans*my_pow(num[i-1],num[i]))%mod;
    }
    printf("%lld",ans);
    return 0;
}