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>
typedef long long ll;
typedef long double ld;
const int INF=1e9,MOD=998244353,ohara=1e6+10;
const ll LINF=1e18;
using namespace std;
    
#define rep(i,n) for(ll (i)=0;(i)<(int)(n);(i)++)
#define rrep(i,a,b) for(ll i=(a);i<(b);i++)
#define rrrep(i,a,b) for(ll i=(a);i>=(b);i--)
#define all(v) (v).begin(), (v).end()
#define Size(n) (n).size()
#define Cout(x) cout<<(x)<<endl
#define doublecout(a) cout<<fixed<<setprecision(15)<<a<<endl;
#define Cerr(x) cerr<<(x)<<endl
#define fi first
#define se second
#define P pair<ll,ll> 
#define m_p make_pair
#define V vector<ll> 
#define U_MAP unordered_map<ll,ll>
#define pq priority_queue<ll>
#define rpq priority_queue<ll,vector<ll>,greater<ll>>
#define p_b push_back
    
ll n,cnt,ans,a[ohara],b,c,d,tmp,tmpp,m,h,w,x,y,sum,pos,k,q;
ld doua;
int dy[]={1,0,-1,0};
int dx[]={0,1,0,-1};
//int dy[]={-1,0,1,-1,1,-1,0,1};
//int dx[]={-1,-1,-1,0,0,1,1,1};
string alph("abcdefghijklmnopqrstuvwxyz"),s;
bool fl;
struct edge{int to,cost;};
ll f[ohara],fr[ohara];
ll dep[ohara];
    
//------ Believe yourself as a genius!!!!!! ------


ll mod_pow(ll xx,ll nn,ll mod){
    ll ret=1;
    while(nn>0){
        if(nn&1)ret=ret*xx%mod;
        xx=xx*xx%mod;
        nn>>=1;
    }
    return ret;
}

ll ncr(ll nn,ll r){
    if(nn<r)return 0;
    return f[nn]*fr[r]%MOD*fr[nn-r]%MOD;
}

ll rui[ohara];
V g[ohara];
ll tyo[ohara];    

int main(void){
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    
    cin>>n;
    rui[1]=1;
    rrep(i,2,n+1){
        rui[i]=rui[i-1]*i;
        rui[i]%=MOD;
    }
    rep(i,n)cin>>a[i],dep[a[i]]++;
    sort(a,a+n);
    if(a[0]!=0||a[1]==0){
        Cout(0);
        return 0;
    }
    rep(i,n-1){
        if(a[i]==a[i+1]||a[i]+1==a[i+1])continue;
        Cout(0);
        return 0;
    }
    ans=1;
    rep(i,n){
        if(a[i]==0)continue;
        ans*=a[i];
        ans%=MOD;
    }
    Cout(ans);
    return 0;
}