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 FOR(i,a,b) for(int (i) = (a);(i) < (b);i++)
#define REP(i,n) FOR(i,0,n)
typedef long long ll;
const ll MOD = 998244353;

ll POW(ll x,ll y){
    ll res = 1;
    for(int i = 0;i < y;i++){
        res *= x;
        res %= MOD;
    }
    return res;
}

int main(){
    ll n;
    cin >> n;
    vector<ll> d(n,0);
    REP(i,n){
        int x;
        cin >> x;
        d[x]++;
    }
    int s = 1;
    ll ans = 1;
    bool judge = true;
    if(d[0] != 1){
        cout << 0 << endl;
        return 0;
    }
    for(int i = 1;s < n;i++){
        s += d[i];
        ans *= POW(d[i-1],d[i]);
        ans %= MOD;

    }
    if(judge)cout << ans << endl;
    else cout << 0 << endl;
}