You are given an integer number n. The following algorithm is applied to it:

  1. if n = 0, then end algorithm; 
  2. find the smallest prime divisor d of n; 
  3. subtract d from n and go to step 1. 



Determine the number of subtrations the algorithm will make.

Input

The only line contains a single integer n (2 ≤ n ≤ 10^{10}).

Output

Print a single integer — the number of subtractions the algorithm will make.

Examples

Input


5


Output


1


Input


4


Output


2

Note

In the first example 5 is the smallest prime divisor, thus it gets subtracted right away to make a 0.

In the second example 2 is the smallest prime divisor at both steps.
import math;
n=int(input());
i=2;
p=[]
x=0;
for i in range(2,n+1):
    if i not in p:
        if (n%i==0):
            x=i;
            break;
        j=i*i;
        for j in range(n+1, i):
            p.append(j)
if(x==0):
    x=1;
y=n/x+n%x;
print(int(y));