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 SieveOfEratosthenes(n, arr):
#    prime = [True for i in range(n + 1)]
#    p = 2
#    while (p * p <= n):
#        if (prime[p] == True):
#            for i in range(p * 2, n + 1, p):
#                prime[i] = False
#        p += 1
#    prime[0] = False
#    prime[1] = False
#    for p in range(n + 1):
#        if prime[p]:
#            arr.append(p)
#n = int(raw_input())
#arr = []
#SieveOfEratosthenes(n, arr)
#ans = []
#if n%2==0:
#    while sum(ans)!=n:
#        ans.append(2)
#    print len(ans)
#    print " ".join(map(str, ans))
#else:
#    while sum(ans)!=(n-3):
#        ans.append(2)
#    ans.append(3)
#    print len(ans)
#    print " " . join(map(str, ans))

##n = int(input())
#if n==2:
#    print("1")
#    print("2")
#elif n==3:
#    print("1")
#    print("3")
#ans = []
#if n%2==0 and n>3:
#   while sum(ans)!=n:
#       ans.append(2)
#   print " ".join(map(str, ans))
#lse:
#   while sum(ans)!=(n-3):
#       ans.append(2)
#   ans.append(3)
#   print len(ans)
#   print " " . join(map(str, ans))

n = int(input())
if n==2:
    print("1")
    print("2")
elif n==3:
    print("1")
    print("3")
elif n%2==0 and n>3:
    print(n//2)
    for i in range(n//2):
        print("2", end=" ")
elif n%2==1 and n>3:
    print(n//2)
    for i in range((n//2)-1):
        print("2", end=" ")
    print("3")