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:
// Generated by CoffeeScript 1.10.0
(function() {
  var arr, i, j, n, ref, ref1, results, results1;

  n = Number(readline());

  if (n % 2 === 1) {
    arr = (function() {
      results = [];
      for (var i = 0, ref = (n - 3) / 2; 0 <= ref ? i < ref : i > ref; 0 <= ref ? i++ : i--){ results.push(i); }
      return results;
    }).apply(this).map(function(x) {
      return '2';
    });
    arr.push(3);
  } else {
    arr = (function() {
      results1 = [];
      for (var j = 0, ref1 = n / 2; 0 <= ref1 ? j < ref1 : j > ref1; 0 <= ref1 ? j++ : j--){ results1.push(j); }
      return results1;
    }).apply(this).map(function(x) {
      return '2';
    });
  }

  print(arr.length);

  print(arr.join(' '));

}).call(this);