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 PYTHON):

Solution:
num = input()

if num == 3:
    print 1
    print 3
elif num % 2 == 0:
    print num/2

    dag = ''
    for i in range(0,num/2-1):
        dag += '2'
        dag += ' '
    dag+='2'
    print dag
else:
    num-=3
    print num/2+1
    dag = ''
    for i in range(0,num/2-1):
        dag += '2'
        dag += ' '
    dag+='2'
    dag+=' '
    dag+='3'
    print dag