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())
v=[]
for i in range(2, n+1, 1):
    divisor=0
    for k in range(2, int(pow(i,1/2)+1), 1):
        if i%k==0:
            divisor+=1
            break
    if divisor==0:
        v.append(i)
        #print(v)
ans=0
k=0
ans2=''
for j in v:
    while k+j<=n and n-(k+j)!=1:
        ans+=1
        ans2+=str(j)
        k+=j
        if(k!=n):
            ans2+=' '
print(ans)
print(ans2)