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:
"""
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.
"""
n = int(input())
array = []

i = 0
while n > 1:
    if n != 3:
        n -= 2
        i += 1
        array += [2]
    elif n == 3:
        n -= 3
        i += 1
        array += [3]

print(i)
for i in array:
    print(i,end=" ")