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:
import bisect
import sys
import fileinput

def getPrimes():
    primes = []
    values = [True for p in range(2, (10**6) + 10)]
    p = 2
    while p <= (10**6):
        if values[p] == True:
            primes.append(p)
            for m in range(p*2, (10**6), p):
                values[m] = False
        p += 1
    del values
    return primes

a = int(input(""))
arr = []
primes = getPrimes()
minimum = 0
if a > 3:
    while a > 0:
        arr.append(primes[minimum])
        a -= primes[minimum]
        if a == 3:
            minimum += 1
        if a == 0:
            break
else:
    arr = [a]

print(len(arr))
print (" ".join([str(word) for word in arr]))