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>
using namespace std;


int main(){
    int N;
    cin >> N;
    vector<int> D(N);
    for(int i=0;i<N;i++){
        cin >> D.at(i);
    }

    int count,prev_count, ans;
    count = 0;
    prev_count = 0;
    int num;
    num = 0;
    while(true){

        prev_count = count;
        count = 0;
        for(int i=0;i<D.size();i++)
        {
            if(D.at(i) == num)
            {
                count++;
            }
        }

        if(num != 0 && count == 0)
        {
            for(int j=0;j<D.size();j++)
            {
                if(D.at(j) > num){
                    cout << 0;
                    return 0;
                }

            }
            break;
        }

        if(num == 0 && count != 1){
            cout << 0;
            return 0;
        }

        if(num == 0){
            ans = 1;
        }else{
            ans = ans * pow(prev_count,  count);
        }

        num++;
        if(num == N){
            break;
        }

    }
    if(ans >= 998244353)
        ans = ans % 998244353;
    cout << ans;

    return 0;
}