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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func scanInt() int {
	sc.Scan()
	iv, _ := strconv.Atoi(sc.Text())
	return iv
}

func init() {
	sc.Split(bufio.ScanWords)
}

func main() {
	n := scanInt()
	xm := make(map[int]int)
	d0 := scanInt()
	xm[d0]++
	if d0 > 0 {
		fmt.Println(0)
	}

	for i := 0; i < n-1; i++ {
		d := scanInt()
		xm[d]++
	}
	if xm[0] > 1 {
		fmt.Println(0)
	}

	const mod = 998244353
	ans := 1
	for k, v := range xm {
		if k == 0 {
			continue
		}
		for i := 0; i < v; i++ {
			ans *= xm[k-1]
			ans %= mod
		}
	}
	fmt.Println(ans)
}