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:
n = int(input())
c = n // 2
c-=1
if n%2==1:
    c-=1
st='2' if c>=0 else ""
for i in range(c):
    st+=' 2'
print(c+1) if n%2==0 else print(c+2)
if st=='':
    print(3)
else:
    print(st+' 3') if n%2==1 else print(st)