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)

m = 998244353
def myPow(a,b):
    a %= m
    if b == 1:
        return a%m
    elif b == 0:
        return 1
    if b%2 == 0:
        return myPow(a**2,b//2)%m
    else:
        return (a%m)*myPow(a**2,(b-1)//2)%m

n = int(input())
ngo = [0]*n
d = list(map(int,input().split()))
for i in range(n):
    ngo[d[i]]+=1
if ngo[0] != 1:
    print(0)
    exit(0)
ans = 1
for i in range(n-1):
    ans = (ans*myPow(ngo[i],ngo[i+1])%m)%m
print(ans%m)