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())
# prime = [True for i in range(n + 1)];
# prime[0] = False
# prime[1] = False
# for i in range(2,n + 1):
#     if prime[i]:
#         j = i**2
#         while (j < n + 1):
#             prime[j] = False
#             j += i
res = 1
list = []
while n != 3 and n != 2:
    n -= 2
    list.append(2)
    res += 1
list.append(n)
print(res)
for x in list:
    print(x, end = " ")