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;

typedef long long ll;
#define rep(i, n) for(int i = 0; i < n; i++)

const ll mod = 998244353;

//a^bにおいて、numがa、mulがbである
ll func(ll num, ll mul){
    ll val = 1;
    rep(i, mul){
        val = (val * num) % mod;
    }
    return val;
}

int main(){
    ll N;
    cin >> N;
    vector<ll> d(N);
    vector<ll> dist(N);
    rep(i, N) cin >> d[i];
    ll ans = 1;
    
    //d[0] != 0であるときは、終了
    if(d[0] != 0){
        cout << 0 << endl;
        return 0;
    }
    //頂点1からの距離をインデックスの値にした配列
    //頂点からの距離がiの頂点が何個あるのかを格納
    rep(i, N) dist[d[i]]++;
    for(int i = 0; i < N-1; i++){
        ans = (ans * func(dist[i], dist[i+1])) % mod;
    }
    cout << ans << endl;
    return 0;
}