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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<cstdio>
using namespace std;
#define LL long long
const int CN = 1e5+5;
const LL R = 998244353;
int n,fir; LL s[CN];
LL qpow(LL a,LL b){
    LL rec = 1;
    while(b){
        if(b & 1) (rec *= a) %= R;
        (a *= a) %= R; b >>= 1;
    }
    return rec;
}
int main(){
    scanf("%d%d",&n,&fir);
    for(int i=2;i<=n;i++) {int x; scanf("%d",&x); s[x]++;}

    if(fir) printf("0");
    else{
        LL ans = 1;
        for(int i=2;i<=n;i++) (ans *= qpow(s[i-1], s[i])) %= R;
        printf("%lld",ans);
    }
}