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++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;

#define N 100005

int d[N], n, cnt[N], mx;

const int mod = 998244353;

int main() {
	scanf("%d", &n);
	for (int i = 1; i <= n; i ++) {
		scanf("%d", &d[i]);
        cnt[d[i]] ++;
        mx = max(mx, d[i]);
	}
    for (int i = mx; i >= 0; i --) if (cnt[i] == 0) return puts("0"), 0;
    if (cnt[0] > 1) return puts("0"), 0;
    int ans = 1;
    for (int i = 1; i <= n; i ++) {
        int k = d[i];
        if (k>0) ans = 1ll * ans * cnt[k-1] % mod;
    }
    cout << ans << endl;
	return 0;
}