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;

long long modPow(long long a, long long n, long long waru) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) { res = res * a % waru; }
        a = a * a % waru;
        n >>= 1;
    }

    return res;
}

int main() {
    //
    long long waru = 998244353;
    long long num;
    long long kekka = 1;
    long long pre = 0;

    map<long long, long long> m;

    cin >> num;
    for (int i = 0; i < num; i++) {
        long long tmp;
        cin >> tmp;
        m[tmp]++;
    }

    for (auto itr : m) {
        if (itr.first == 0) {
            if (itr.second == 1) {
                pre = 1;
                break;
            } else {
                cout << 0 << endl;
                return 0;
            }
        } else {
            cout << 0 << endl;
            return 0;
        }
    }

    for (auto itr : m) {
        if (itr.first == 0) continue;
        if (itr.first == 1) {
            pre = itr.second;
            continue;
        }
        kekka *= modPow(pre, itr.second, waru);
        kekka = kekka % waru;
        // kekka *= (long long)pow(pre, itr.second) % waru;
        pre = itr.second;
    }

    cout << kekka << endl;
    //
}