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 <math.h>
#include <string.h>
#include <limits.h>

#define DIV 998244353

//高速べき乗(mod DIV)
long long mypow(long long k, long long n) {
	long long temp = 1;

	k = k % DIV;
	while (n) {
		if (n % 2) temp = temp * k % DIV;
		k = k * k % DIV;
		n = n / 2;
	}
	return temp % DIV;
}

int main(void) {
	long long n;
	long long d[100000] = { 0 };
	long long ans = 1, max = 0;
	long long cnt[100000] = { 0 };

	scanf("%lld", &n);
	for (int i = 0; i < n; i++) {
		scanf("%lld", &d[i]);
		cnt[d[i]]++;
		if (max < d[i])max = d[i];
	}
	for (int i = 1; i <= max; i++) ans = (ans * mypow(cnt[i - 1], cnt[i]))%DIV;
	printf("%lld", ans);
	return 0;
}