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())
a = []
i = 2
k = 2
while n > 0:
    if n - (n//i)*i != 1:
        for j in range(n//i):
            a.append(i)
        n -= (n//i)*i
    else:
        for j in range(n//i - 1):
            a.append(i)
        n -= (n//i - 1)*i
    b = i
    while True:
        b += 1
        ans = "p"
        j = 1
        while j *j <= n:
            j += 1
            if b % j == 0:
                ans = "c"
                break
        if n == 2: ans = "p"
        if ans == "p":
            i = b
            break
    if i >= n and n != 0:
        a.append(n)
        break
print(len(a))
ans = ""
for i in a: ans += str(i) + " "
print(ans)