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 JAVA):

Solution:
var res = sol(readline(), readline());
print(res);

function sol(line1) {
    var input1 = line1.split(" ").map((x) => Number(x));

    var n = input1[0];

    var result = [];

    while (n > 3) {
        n -= 2;
        result.push(2);
    }

    result.push(n);

    return result.length + "\n" + result.join(" ");
}