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 Scala (2.11.7) (judge verdict: Wrong Answer)

object Main extends App {
  val n =  scala.io.StdIn.readInt()
  val d = scala.io.StdIn.readLine()
  val dArray = d.split(" ").map(_.toLong).toVector
  if(dArray(0) != 0L) {
    println(0)
  } else {
    var before = 0L
    println(dArray.tail.foldLeft(1L) { case (sum, d) =>
      if ( d == 0) {
        sum * 0
      } else if (before != 0 && before > d) {
        sum * 0
      } else {
        before = d
        sum * d % 998244353L
      }
    })
  }
}