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 = long long;

const int maxn = 1e5+5;
const int M = 998244353;
int n, d[maxn];
int cnt[maxn];

int main() {
    ios_base::sync_with_stdio(false); cin.tie(NULL);
    cin >> n;
    for (int i = 0; i < n; i++) {
        cin >> d[i];
    }
    sort(d,d+n);
    if (d[0] != 0 || (n > 1 && d[1] == 0)) {
        cout << 0 << '\n';
        return 0;
    }
    cnt[0] = 1;
    int ans = 1;
    for (int i = 1; i < n; i++) {
        ans = (1LL*ans*cnt[d[i]-1]) % M;                
        cnt[d[i]]++;
    }
    cout << ans << '\n';
}