Bachgold Problem !!!

 PROBLEM 5: Bachgold Problem

      Problem Reference : Codeforces   

Bachgold problem is very easy to formulate. Given a positive integer n represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than 1.

Recall that integer k is called prime if it is greater than 1 and has exactly two positive integer divisors — 1 and k.

Input:

The only line of the input contains a single integer n (2 ≤ n ≤ 100 000).

Output:

The first line of the output contains a single integer k — maximum possible number of primes in representation.

The second line should contain k primes with their sum equal to n. You can print them in any order. If there are several optimal solution, print any of them.

Solution:

1. import sys
2. n = int(input())
3. cnt = 0
4. l = []
5. if n == 3:
6. print('1')
7. print('3')
8. sys.exit()
10. if n % 2 == 0:
11. while n > 0:
12. cnt+=1
13. n = n - 2
14. l.append('2')
15. print(cnt)
16. for j in l:
17. print(j,end=' ')
18. else:
19. while n > 0:
20. cnt+=1
21. n = n - 2
22. l.append('2')
23. if n == 3:
24. n = n - 3
25. cnt+=1
26. l.append('3')
27. break
28. print(cnt)
29. for j in l:
30. print(j,end=' ')

The above solution is in python language.

Examples

input

5

output

2
2 3

input

6

output

3
2 2 2