Problem: 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.

Examples

Input

5


Output

2
2 3


Input

6


Output

3
2 2 2

Solution (in PYTHON3):

Solution:
x=int(input())
p=[]
x1=x
a=x//2
print(a)
for i in range (int(a)):
    p.append("2")    
if x1%2==0:  
    for i in p:
        print(i,"",end="")        
else :
    k=int(p[-1])+1
    del(p[-1])
    for i in p:
        print(i,"",end="")
    print(k)