Divisor Subtraction

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.

inputFormat

Input

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

outputFormat

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.

样例

4

2

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