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 Rust (1.15.1) (judge verdict: Wrong Answer)

use std::io::*;
use std::str::FromStr;

/* 
The read function reads a string according to each one. 
*/
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char) 
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

fn exp(m:i64,n:i64)->i64{
    let mut sum: i64 = 1;
    let div: i64 = 998244353;
    let m: i64 = m as i64 % div;
    for _i in 0..n{
	sum *= m;
	if sum >= div {
	    sum%=div;
	}
    }
    if m==0{
	sum = 0;
    }
    sum%=div;
    sum
}
//main function
fn main() {
    let n: usize = read();
    let mut vbox:Vec<i64> = Vec::with_capacity(n);
    let mut sum: i64 = 1;
    let mut flag: bool = true;
    let div: i64 = 998244353;
    unsafe{
	vbox.set_len(n);
    }
    for i in 0..n{
	vbox[i as usize] = 0;
    }
    for _i in 0..n{
	let number:usize = read();
	vbox[number] += 1;
    }
    for i in 1..n{
	if !flag && vbox[i as usize]!=0 {
	    println!("0");
	    return;
	}else if vbox[i as usize]==0{
	    flag = false;
	}
	
	if flag{
	    sum *= exp(vbox[i as usize -1],vbox[i as usize]);
	}
	if sum>=div{
	    sum %=div;
	}
    }
    println!("{}",sum);
}