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>

int main(){
   int i,n,d[100000],j,jj,k;
   long a;
 
   scanf("%d",&n);
   for (i=0;i<n;i++) scanf("%d",&d[i]);
   j=0;
   for (k=1;k<n;k++)
      if (d[k]==1) j++;
   if (j==0 || d[0]!=0) {
      puts("0");
      return 0;
   }
   a=1;
   for (i=2;i<n;i++) {
      jj=0;
      for (k=1;k<n;k++)
         if (d[k]==i) jj++;
      if (jj==0) break;
      for (k=0;k<jj;k++) a=(a*j)%998244353;
      j=jj;
   }
   printf("%ld\n",a);
   return 0;
}