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 ll long long
#define rep(i, n) for(ll i=0; i<n; i++)
#define repr(i, s, e) for(ll i=s; i>=e; i--)
#define reps(i, s, e) for(ll i=s; i<=e; i++)
#define inf 1e18
#define all(v) v.begin(),v.end()
#define vsort(v) sort(v.begin(), v.end())
#define vsortr(v) sort(v.begin(), v.end(), greater<ll>())
#define ceil(a, b) (a+b-1)/b
#define ok cout << "ok" << endl;
#define sp << " " <<
template<typename A, size_t N, typename T> void Fill(A (&array)[N], const T &val){ fill((T*)array, (T*)(array+N), val); }
template<typename T> inline bool chmax(T &a, T b){ if(a<b){ a=b; return true; } return false; }
template<typename T> inline bool chmin(T &a, T b){ if(b<a){ a=b; return true; } return false; }
template<typename T> void vdebug(vector<T> v){ cout << "vdebug" << endl; for(auto vv : v){ cout << vv << " "; } cout << endl; }
template<typename T> void adebug(T arr[], ll n){ cout << "adebug" << endl; reps(i, 0, n){ cout << arr[i] << " "; } cout << endl; }
template<typename T1, typename T2> void mdebug(map<T1, T2> mp){ cout << "mdebug" << endl; for(auto const& m : mp){ cout << m.first sp m.second << endl; }}
template<typename T1, typename T2> void mldebug(multimap<T1, T2> mp){ cout << "mldebug" << endl; for(auto const& m : mp){ cout << m.first sp m.second << endl; }}
template<typename T1, typename T2> void mdebugr(map<T1, T2, greater<T1>> mp){ cout << "mdebug" << endl; for(auto const& m : mp){ cout << m.first sp m.second << endl; }}
template<typename T1, typename T2> void mldebugr(multimap<T1, T2, greater<T1>> mp){ cout << "mldebug" << endl; for(auto const& m : mp){ cout << m.first sp m.second << endl; }}
void ans(bool b){ if(b) cout << "Yes" << endl; else cout << "No" << endl; }
void ans2(bool b){ if(b) cout << "YES" << endl; else cout << "NO" << endl; }
int dx[] = {1, -1, 0, 0, 1, -1, 1, -1};
int dy[] = {0, 0, 1, -1, 1, -1, -1, 1};


ll mod = 998244353;

int main(){
    ios::sync_with_stdio(false);
    cin.tie(0);

    ll n, d[100010];
    ll cnt[100010];
    Fill(cnt, 0);
    ll maxi = 0;
    cin >> n;
    reps(i, 1, n){
        cin >> d[i];
        cnt[d[i]]++;
        maxi = max(maxi, d[i]);
    }

    if(d[1] != 0){
        cout << 0 << endl;
        return 0;
    }

    ll res = 1;
    reps(i, 0, maxi){
        if(i == 1 || i == 0) continue;
        ll num = long(pow(cnt[i-1], cnt[i]))%mod;
        res *= pow(cnt[i-1], cnt[i]);
        res %= mod;
    }

    cout << res << endl;

    return 0;
}