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<math.h>

int main(){
    long long int mod = 998244353;
    int n;
    scanf("%d", &n);
    int d[n];
    long long int t[n], p[n];
    for(int i=0; i<n; i++){
        t[i] = 0;
        p[i] = 1;
    }
    for(int i=0; i<n; i++){
        scanf("%d", &d[i]);
    }
    for(int i=0; i<n; i++){
        t[d[i]]++;
    }
    for(int i=1; i<n; i++){
        long long int z = t[i-1];
        for(long long int j=1; j<t[i]; j++){
            z = ((z%mod) * (t[i-1]%mod))%mod;
        }
        if(t[i] == 0){
            p[i] = 0;
        }else{
        p[i] = z;
        }
    }
    if(d[0] != 0){
        printf("0");
    }else{
        int f = 1;
        int x = 0;
        for(int i=1; i<n; i++){
            if(t[i] > 0){
                if(x != i-1){
                    f = 0;
                }
                x = i;
                //p[i] = ((p[i-1]%mod) * (p[i]%mod))%mod;
                long long int s = 0;
                for(int j=0; j<p[i]; j++){
                    s += p[i-1];
                    s = s%mod;
                }
                p[i] = s;
            }
        }
        if(f){
        printf("%lld", p[x]);
        }else{
            printf("0");
        }
    }

    return 0;
}