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 <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <cmath>
#include <stdio.h>
#include <queue>
#include <climits>
#include <map>
#include <set>
const int mod = 1e9 + 7;
const int inf = 1 << 20;
const long long INF = 1LL << 60;
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
using namespace std;

ll m = 998244353;

ll pow(ll a,ll k)
{
    for(ll i = 0; i < k; i++){
        a *= a;
        a %= m;
    }
    return a;
}


int main()
{
    int n;
    cin >> n;
    int d[n];
    ll ans = 1;
    int a = 0;
    for(int i = 0; i < n; i++){
        d[i] = 0;
    }
    
    for(int i = 0; i < n; i++){
        int k;
        cin >> k;
        a = max(k,a);
        d[k]++;
    }
    if(d[0] != 1){
        cout << 0 << endl;
        return 0;
    }else{
        for(int i = 1; i < a; i++){
            ans *= pow(d[i],d[i+1]);
            ans %= m;
        }
        cout << ans << endl;
    }
}