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 (1.6) (judge verdict: Runtime Error)

package main

import(
    "fmt"
    "sort"
    "math"
)

func main() {
    var n int
    var num []int
    
    fmt.Scan(&n)
    for i:=0;i < n;i++ {
        var d int
        fmt.Scan(&d)
        num = append(num, d)
    }
    if num[0] != 0 {
        fmt.Println(0)
        return
    }
    sort.Ints(num)
    count, flag := counter(num)
    if !flag {
        fmt.Println(0)
        return
    }
    fmt.Println(result(count))
}

func counter(num []int) ([]int, bool){
    var count []int
    var n int
    
    for i:=1;i < len(num);i++ {
        for  {
            if num[i] > num[i-1] {
                count = append(count, n)
                if num[i] > num[i-1]+1 {
                    return count, false
                }
                break
            }else if i >= len(num) {
                break
            }else {
                n++
                i++
            }
        }
        n = 1
    }
    count = append(count, n)

    return count, true
}

func result(count []int) int {
    result := 1
    for i:=2;i < len(count);i++ {
        result *= pow(count[i-1], count[i])
    }
    return result
}

func pow(p, q int) int {
    return int(math.Pow(float64(p), float64(q)))
}