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 <vector>
#define rep(i, n)   for(int i = 0; i < (n); i++)
#define MOD 998244353
using namespace std;
typedef long long ll;

int main(){
    int n;  cin >> n;
    vector<int>d(n);
    int max = 0;
    rep(i, n){
        int tmp;    cin >> tmp;
        if(max < tmp)   max = tmp;
        if(i==0&&tmp!=0){
            cout << 0 << endl;
            return 0;
        }
        d[tmp]++;
    }
    ll ans = 1;
    for(int i = 1; i <= max; i++){
        rep(j, d[i])    ans *= i;
        ans %= MOD;
    }
    cout << ans << endl;
}