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().split()))
db = [0] * n
MOD = 998244353

#距離iの頂点の数をdb[i]に保存
for i in range(n):
    db[d[i]] += 1

#末尾に連続する0を削除
if (db[n-1] == 0):
    l = n-1
    for i in range(1,n):
        tmp = db[n-i]
        if (tmp == 0) : l = n-i 
        else : break
    
    del db[l:n]


if (d[0] != 0)|(db[0] != 1):
    print(0)
    exit()
if (len(db) <= 2):
    print(len(db)-1)
    exit()

db.append(1)
ans = 1

for i in range(len(db)-1):
    tmp = (db[i]**db[i+1]) % MOD
    ans *= tmp

print(ans)