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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#define M 998244353
typedef long long ll;
ll power(int a, int b){
    ll seki = a;
    for(int i=0;i<b-1;i++){
        seki *= a;
        seki %= M;
    }
    return seki;
}
int main(void){
    int N;
    scanf("%d",&N);
    int array[100001]={0};
    int x;
    int count=0;
    for(int i=0;i<N;i++){
        scanf("%d",&x);
        if(array[x]==0) count++;
        array[x]++;
    }
    
    if(array[0]!=1){
        printf("0\n");
    }else{
        ll ans = 1;
        for(int i=1;i<count-1;i++){
            if(array[i]==0||array[i+1]==0){
                ans = 0;
                break;
            }
            ans *= power(array[i],array[i+1]);
            ans %= M;
        }
        printf("%lld\n",ans);
    }
    return 0;
}