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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>

#define rep(i, n) for(int i=0;i<(int)(n);i++)
#define MOD 998244353

//compare function (ascending order)
//qsort(array, n, size, cmp)
int cmp(const void *a,const void *b){ 
    if(*(int*)a < *(int*)b){
        return -1;
    }
    else if(*(int*)a == *(int*)b){
        return 0;
    }
    return 1;
}

int main(void){
	int n;
	int i;
	scanf("%d",&n);
	int d[n];
	int cntp=1, cnta=1;
	long ans=1;
	rep(i,n){
		scanf("%d",&d[i]);
	}
	if(d[0] != 0){
		printf("0\n");
		return 0;
	}
	qsort(d, n, sizeof(d[0]), cmp);
/*	rep(i,n){
		printf("%d",d[i]);
	}
	printf("\n");	*/
	for(i=1;i<n;i++){
		if(d[i]-d[i-1] != 1 && d[i]-d[i-1] != 0){
			printf("0\n");
			return 0;
		}
		if(d[i] == d[i+1] && i != n-1){
			cnta++;
		}
		else{
			ans = ans*pow(cntp, cnta);
			ans = ans % MOD;
			cntp = cnta;
			cnta = 1;
		}
	}
	printf("%ld\n",ans);
    return 0; 
}