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>
#define int long long 
using namespace std;
const int HA=998244353;
const int N = 1e5 + 10;
int n , maxs = -1;
int buck[N];
inline int ksm ( int x , int y ) {
	int res = 1;
	while ( y ) {
		if ( y & 1 ) 
			res = ( x * res ) % HA;
		x = ( x * x ) % HA;
		y >>= 1; 
	}
	return res % HA;
}
signed main ( void ) {
	ios :: sync_with_stdio(false);
	cin.tie(0),cout.tie(0);
	cin>>n;
	for(int i=1;i<=n;i++){
		int x;
		cin>>x;
		buck[x]++;
		maxs = max ( maxs , x );
	}
	int rec = 1;
	for ( int i = 0 ; i < maxs ; i++ ) 
		rec = ( rec * ksm ( buck[i] , buck[i + 1] ) ) %HA;
	printf ( "%lld\n" , rec );
	return 0;
}