Problem: Dima loves representing an odd number as the sum of multiple primes, and Lisa loves it when there are at most three primes. Help them to represent the given number as the sum of at most than three primes.

More formally, you are given an odd numer n. Find a set of numbers pi (1 ≤ i ≤ k), such that

  1. 1 ≤ k ≤ 3
  2. pi is a prime
  3. <image>



The numbers pi do not necessarily have to be distinct. It is guaranteed that at least one possible solution exists.

Input

The single line contains an odd number n (3 ≤ n < 109).

Output

In the first line print k (1 ≤ k ≤ 3), showing how many numbers are in the representation you found.

In the second line print numbers pi in any order. If there are multiple possible solutions, you can print any of them.

Examples

Input

27


Output

3
5 11 11

Note

A prime is an integer strictly larger than one that is divisible only by one and by itself.

Solution (in JAVA):

Solution:
	import java.io.*;
import java.math.*;
import java.nio.file.attribute.AclEntry.Builder;
import java.security.KeyStore.Entry;
import java.util.*;
	 
	 
	public   class CODEFORCES {
		private InputStream is;
		private PrintWriter out;
		int time = 0, dp[][], DP[], start[], end[], dist[],  black[], MOD = (int)(1e9+7), arr[], weight[][], x[], y[];
		int MAX = 800000, N, K, L;
		long red[];
		ArrayList<Integer>[] amp;
		boolean b[], boo[][];
		Pair prr[], parent[][];
		HashSet<Integer> hs = new HashSet<>();
		long Dp[][][][] = new long[110][110][12][12];
	 
		public static void main(String[] args) throws Exception {
			new Thread(null, new Runnable() {
			public void run() {
				try {
	 
			new CODEFORCES().soln();
			} catch (Exception e) {
					System.out.println(e);
				}
			}
		}, "1", 1 << 26).start();
			//new CODEFORCES().soln();
		}
		char ch[][];
		int ans = 0, cnt = 0;
		int n1, n2, k1, k2;
		void solve() {
			int n = ni();
			ArrayList<Integer> amp = new ArrayList<>();
			if(isPrime(n)){
				out.print(1+"\n" + n);
				return;
			}
			for(int i = 2;i<=1000;i++){
				if(isPrime(i)){
					amp.add(i);
				}
			}
			if(n%2==0) out.println(2);
			if(n%2==1){out.print(3+"\n"); n-=3; out.print(3+" ");}
			for(int i : amp) {
				if(isPrime((n-i))){
					out.print(i+" "+(n-i));
					break;
				}
			}
		}

		boolean isPrime(int x){
			for(int i = 2;i*1L*i<=x;i++) if(x%i==0) return false;
			return true;
		}
		public static class FenwickTree {
			
		    int[] array; // 1-indexed array, In this array We save cumulative information to perform efficient range queries and updates
	 
		    public FenwickTree(int size) {
		        array = new int[size + 1];
		    }
		    public int rsq(int ind) {
		        assert ind > 0;
		        int sum = 0;
		        while (ind > 0) {
		            sum += array[ind];
		            //Extracting the portion up to the first significant one of the binary representation of 'ind' and decrementing ind by that number
		            ind -= ind & (-ind);
		        }
		        return sum;
		    }
		    public int rsq(int a, int b) {
		        assert b >= a && a > 0 && b > 0;
		        return rsq(b) - rsq(a - 1);
		    }
		    public void update(int ind, int value) {
		        assert ind > 0;
		        while (ind < array.length) {
		            array[ind] += value;
		            //Extracting the portion up to the first significant one of the binary representation of 'ind' and incrementing ind by that number
		            ind += ind & (-ind);
		        }
		    }
		    public int size() {
		        return array.length - 1;
		    }
		}
		int  p ;
		void buildGraph(int n){
			for(int i = 0; i<n ;i++){
				int x1 = ni() -1, y1 = ni()-1;
				amp[x1].add(y1);
				amp[y1].add(x1);
				x[i] = x1; y[i] = y1;
			}
		}
		long get(int x){
			long val = 0;
			for(int i = 0; i< N; i++){
				val += Math.abs(x-arr[i]);
				x+=L;
			}
			return val;
		}
		void dfs(int i, int j){
			boo[i][j] = true;
			if(ch[i][j]=='F') return;
			Pair p = new Pair(i,j);
			if(i>0 && ch[i-1][j]!='*' && !boo[i-1][j]){
				parent[i-1][j] = p;
				dfs(i-1,j);
			}
			if(j>0 && ch[i][j-1]!='*' && !boo[i][j-1]){
				parent[i][j-1] = p;
				dfs(i,j-1);
			}
			if(i<N-1 && ch[i+1][j]!='*' && !boo[i+1][j]){
				parent[i+1][j] = p;
				dfs(i+1,j);
			}
			if(j<K-1 && ch[i][j+1]!='*' && !boo[i][j+1]){
				parent[i][j+1] = p;
				dfs(i,j+1);
			}
		}
		void recur(int n, int k){
			if(k<0) return;
			hs.add(K-k);
			if(n>=0 && dp[n][k]!=-1) return;
			if(n>=0) dp[n][k] = 1;
			for(int i = n+1;i<N;i++){
				recur(i,k-arr[i]);
			}
		}
		long modInverse(long a, long mOD2){
	        return  power(a, mOD2-2, mOD2);
		}
		long power(long x, long y, long m)
		{
			if (y == 0)
	    return 1;
		long p = power(x, y/2, m) % m;
		p = (p * p) % m;
	 
		return (y%2 == 0)? p : (x * p) % m;
		}
		public String isPossible(int b[]){
			String ans = "Possible";
			int n = b.length;
			Arrays.sort(b);
			if(n==1) return "Possible";
			if(b[0]==1) return "Impossible";
			if(b[0]>=n) return ans;
			int lcm = 1;
			for(int i : b){
				long gcd = gcd(lcm,i);
				lcm *= (i/gcd);
			}
			int cnt = 0;
			for(int i : b) cnt+=lcm/i;
			if(cnt>lcm) return "Impossible";
			return ans;
		}
		public long gcd(long a, long b){
			if(b==0) return a;
			return gcd(b,a%b);
		}
		void failFn(String str, int arr[]){
			int len = 0;
			arr[0] = 0;
			int i = 1;
			while(i<arr.length){
				if(str.charAt(i)==str.charAt(len)){
					arr[i++] = ++len;
					continue;
				}
				if(len == 0){
					arr[i] = len;
					i++;
					continue;
				}
				if(str.charAt(i)!=str.charAt(len)){
					len = arr[len-1];
				}
			}
		}
		static class ST1{
			int arr[], st[], size;
			ST1(int a[]){
				arr = a.clone();
				size = 10*arr.length;
				st = new int[size];
				build(0,arr.length-1,1);
			}
			void build(int ss, int se, int si){
				if(ss==se){
					st[si] = arr[ss];
					return;
				}
				int mid = (ss+se)/2;
				int val = 2*si;
				build(ss,mid,val); build(mid+1,se,val+1);
				st[si] = Math.min(st[val], st[val+1]);
			}
			int get(int ss, int se, int l, int r, int si){
				if(l>se || r<ss || l>r) return Integer.MAX_VALUE;
				if(l<=ss && r>=se) return st[si];
				int mid = (ss+se)/2;
				int val = 2*si;
				return Math.min(get(ss,mid,l,r,val), get(mid+1,se,l,r,val+1));
			}
		}
		static class ST{
			int arr[],lazy[],n;
			ST(int a){
				n = a;
				arr = new int[10*n];
				lazy = new int[10*n];
			}
			void up(int l,int r,int val){
				update(0,n-1,0,l,r,val);
			}
			void update(int l,int r,int c,int x,int y,int val){
				if(lazy[c]!=0){
					lazy[2*c+1]+=lazy[c];
					lazy[2*c+2]+=lazy[c];
					if(l==r)
						arr[c]+=lazy[c];
					lazy[c] = 0;
				}
				if(l>r||x>y||l>y||x>r)
					return;
				if(x<=l&&y>=r){
					lazy[c]+=val;
					return ;
				}
				int mid = l+r>>1;
				update(l,mid,2*c+1,x,y,val);
				update(mid+1,r,2*c+2,x,y,val);
				arr[c] = Math.max(arr[2*c+1], arr[2*c+2]);
			}
			int an(int ind){
				return ans(0,n-1,0,ind);
			}
			int ans(int l,int r,int c,int ind){
				if(lazy[c]!=0){
					lazy[2*c+1]+=lazy[c];
					lazy[2*c+2]+=lazy[c];
					if(l==r)
						arr[c]+=lazy[c];
					lazy[c] = 0;
				}
				if(l==r)
					return arr[c];
				int mid = l+r>>1;
				if(mid>=ind)
					return ans(l,mid,2*c+1,ind);
				return ans(mid+1,r,2*c+2,ind);
			}
		}
		
		public static int[] shuffle(int[] a, Random gen){
			for(int i = 0, n = a.length;i < n;i++)
			{ 
				int ind = gen.nextInt(n-i)+i; 
				int d = a[i]; 
				a[i] = a[ind];
				a[ind] = d; 
			} 
		return a; 
		}
	 
		class Pair implements Comparable<Pair>{
			int u, v, i;
			Pair(int u, int v){
				this.u = u;
				this.v = v;
			}
			Pair(int u, int v, int i){
				this.u = u;
				this.v = v;
				this.i = i;
			}
			public int hashCode() {
				return Objects.hash();
			}
			/*public boolean equals(Object o) {
				Pair other = (Pair) o;
				return ((u == other.u && v == other.v) || (v == other.u && u == other.v));
			}*/
			public int compareTo(Pair other) {
				//return Integer.compare(val, other.val);
				return Long.compare(u, other.u) != 0 ? (Long.compare(u, other.u)) : (Long.compare(v,other.v));
			}
			public String toString(){
				return this.u +" " + this.v;
			}
		}
		long power(long x, long y, int mod){
			long ans = 1;
			while(y>0){
				if(y%2==0){
					x = (x*x)%mod;
					y/=2;
				}
				else{
					ans = (x*ans)%mod;
					y--;
				}
			}
			return ans;
		}
		void soln() {
			is = System.in;
			out = new PrintWriter(System.out);
			long s = System.currentTimeMillis();
			solve();
			//out.close();
			out.flush();
			//tr(System.currentTimeMillis() - s + "ms");
		}
	 
	 
		// To Get Input
		// Some Buffer Methods
		private byte[] inbuf = new byte[1024];
		public int lenbuf = 0, ptrbuf = 0;
	 
		private int readByte() {
			if (lenbuf == -1)
				throw new InputMismatchException();
			if (ptrbuf >= lenbuf) {
				ptrbuf = 0;
				try {
					lenbuf = is.read(inbuf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (lenbuf <= 0)
					return -1;
			}
			return inbuf[ptrbuf++];
		}
	 
		private boolean isSpaceChar(int c) {
			return !(c >= 33 && c <= 126);
		}
	 
		private int skip() {
			int b;
			while ((b = readByte()) != -1 && isSpaceChar(b))
				;
			return b;
		}
	 
		private double nd() {
			return Double.parseDouble(ns());
		}
	 
		private char nc() {
			return (char) skip();
		}
		private String ns() {
			int b = skip();
			StringBuilder sb = new StringBuilder();
			while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != '
										// ')
				sb.appendCodePoint(b);
				b = readByte();
			}
			return sb.toString();
		}
	 
		private char[] ns(int n) {
			char[] buf = new char[n];
			int b = skip(), p = 0;
			while (p < n && !(isSpaceChar(b))) {
				buf[p++] = (char) b;
				b = readByte();
			}
			return n == p ? buf : Arrays.copyOf(buf, p);
		}
	 
		private char[][] nm(int n, int m) {
			char[][] map = new char[n][];
			for (int i = 0; i < n; i++)
				map[i] = ns(m);
			return map;
		}
	 
		private int[] na(int n) {
			int[] a = new int[n];
			for (int i = 0; i < n; i++)
				a[i] = ni();
			return a;
		}
	 
		private int ni() {
			int num = 0, b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
		private long nl() {
			long num = 0;
			int b;
			boolean minus = false;
			while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'))
				;
			if (b == '-') {
				minus = true;
				b = readByte();
			}
	 
			while (true) {
				if (b >= '0' && b <= '9') {
					num = num * 10 + (b - '0');
				} else {
					return minus ? -num : num;
				}
				b = readByte();
			}
		}
	 
		private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	 
		private void tr(Object... o) {
			if (!oj)
				System.out.println(Arrays.deepToString(o));
		}
	}