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:
a=[]
ans=[]
for i in range(0, 100001, 1):
    a += [True]
for i in range(2, 100001, 1):
    if a[i]:
        for j in range(i * i, 100001, i):
            if j<100001:
                a[j]=False
n=int(input())
i=2
while n != 0:
    if a[i] and n-i!=1:
        n-=i
        ans+=[i]
    else:
        i+=1
print (len(ans))
for i in range(0, len(ans), 1):
    if i!=0:
        print (" ", end="")
    print (ans[i], end="")