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:
import time

def printResult(ct2, ct3):
    nstr =[]

    for x2 in range(ct2):
        nstr.append("2")
    for x3 in range(ct3):
        nstr.append("3")

    print(len(nstr))
    print(" ".join(nstr))

def calculateMaxPrimes(num):
    isEven = num % 2
    ct2 = 0
    ct3 = 0

    if isEven > 0:
        ct2 = (num - 3) // 2
        ct3 = 1
    else:
        ct2 = num // 2

    printResult(ct2, ct3)


def solve():
    num = int(input())
    calculateMaxPrimes(num)

    # print("%fs" % (time.time() - start_time))


solve()