Problem:
Score : 100 points

Problem Statement

How many ways are there to choose two distinct positive integers totaling N, disregarding the order?

Constraints

1 \leq N \leq 10^6

N is an integer.

Input

Input is given from Standard Input in the following format:

N

Output

Print the answer.

Sample Input 1

4

Sample Output 1

1

There is only one way to choose two distinct integers totaling 4: to choose 1 and 3. (Choosing 3 and 1 is not considered different from this.)

Sample Input 2

999999

Sample Output 2

499999

Solution in Python (3.4.3) (judge verdict: Runtime Error)

N = int(input())
D = list(map(int, input().strip().split()))
D.sort()
# print(D)
 
def calc(arr):
  if arr[0] != 0:
    return 0
  result = 1
  curCount = 1
  preCount = 1
  for i in range(1, len(arr)):
    if arr[i] == 0:
      return 0
    if arr[i] == arr[i-1]:
      curCount += 1
    elif arr[i] == arr[i-1] + 1:
      preCount = curCount
      curCount = 1
    else:
      return 0
    result = result * preCount
    if result > 998244353:
      result = result % 998244353
    #print(pre, curCount, preCount, result)
  return result%998244353
 
print(calc(D))