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:
def init():
    vis = [True] * 101
    vis[0] = vis[1] = 0
    for i in range(2,101,1):
        if vis[i]:
            for j in range(i+i,101,i):
                vis[j]=0
    for i in range (0,101,1):
        if vis[i]:
            print(i,end = " ")

a = int(input())
k = a//2
print(k)
for i in range(k-1):
    print(2,end=" ")
print(a%2+2)