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;
using ll = unsigned long long int;

ll n;
vector<ll> d;

void input() {
    cin >> n;
    d = vector<ll>(n);
    for(int i = 0; i < n; i++) {
        cin >> d.at(i);
    }
}

void solve() {
    ll result = 1;
    vector<ll> count(n);
    sort(d.begin(), d.end());
    for(int i = 0; i < n; i++ ) {
        count[d.at(i)]++;
    }
    //for(auto e : count) {
    //    cout << e << endl;
    //}
    if(count[0] != 1) {
        cout << "0" << endl;
        return;
    }
    ll max = *max_element(count.begin(), count.end());
    //cout << max << endl;
    for(ll i = 1; i <= max; i++) {
        result = result * static_cast<ll>(pow(count.at(i-1), count.at(i)));
        result = result % 998244353;

    }
    cout << result << endl;
}
int main() {
    input();
    solve();
}