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;

#define rep(i, a, b) for(int i = (a); i < (b); ++i)
#define trav(a, x) for(auto& a : x)
#define pb push_back
#define mp make_pair
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define endl '\n'

typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;

const ll mod=1000000007;
//head

int main()
{
    ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
    int n;
    cin >> n;
    vll occ(n,0);
    ll a;
    cin >> a;
    if(a != 0) {
        cout << 0 << endl;
        return 0;
    }
    ll maxi = -1;
    occ[0]++;
    for(int i = 0; i < n - 1; i++) {
        cin >> a;
        occ[a]++;
        maxi = max(maxi, a);
    }
    ll ans = 1;
    for(ll i = 1; i <= maxi; i++) {
        ll p = 1;

        for(int j = 0; j < occ[i]; j++) {
            p *= occ[i-1];
        }
        ans *= p;
    }
    cout << ans << endl;
    return 0;
}