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:
def IsPrime(n):
    if n==0 or n==1 or n%2==0:
        return False
    if n==2:
        return True
    for i in range(2,n):
        if n%i==0:
            break
    if i==n-1 and n%i!=0:
        return True
    else:
        return False

n=int(raw_input())
nums=[]

for i in range(n/2):
    nums.append(2)


summ=(2*(n/2))+(n%2)
q=n/2
rem=n%2
i=1

while True and n%2!=0:
    #print rem,summ,q
    if summ==n and IsPrime(rem):
        nums.append(rem)
        break
    nums.remove(2)
    rem=2*i+n%2
    q-=1
    summ=(2*q)+(rem)
    i+=1

print len(nums)
num=''
for i in nums:
    num+=str(i)+' '
print num