Mike has a sequence A = [a1, a2, ..., an] of length n. He considers the sequence B = [b1, b2, ..., bn] beautiful if the gcd of all its elements is bigger than 1, i.e. <image>. 

Mike wants to change his sequence in order to make it beautiful. In one move he can choose an index i (1 ≤ i < n), delete numbers ai, ai + 1 and put numbers ai - ai + 1, ai + ai + 1 in their place instead, in this order. He wants perform as few operations as possible. Find the minimal number of operations to make sequence A beautiful if it's possible, or tell him that it is impossible to do so.

<image> is the biggest non-negative number d such that d divides bi for every i (1 ≤ i ≤ n).

Input

The first line contains a single integer n (2 ≤ n ≤ 100 000) — length of sequence A.

The second line contains n space-separated integers a1, a2, ..., an (1 ≤ ai ≤ 109) — elements of sequence A.

Output

Output on the first line "YES" (without quotes) if it is possible to make sequence A beautiful by performing operations described above, and "NO" (without quotes) otherwise.

If the answer was "YES", output the minimal number of moves needed to make sequence A beautiful.

Examples

Input

2
1 1


Output

YES
1


Input

3
6 2 4


Output

YES
0


Input

2
1 3


Output

YES
1

Note

In the first example you can simply make one move to obtain sequence [0, 2] with <image>.

In the second example the gcd of the sequence is already greater than 1. 
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;


import java.util.ArrayList;
import java.util.Arrays;


public final class CF_410_GCD{

	static void log(int[] X){
		int L=X.length;
		for (int i=0;i<L;i++){
			logWln(X[i]+" ");
		}
		log("");
	}


	static void log(long[] X){
		int L=X.length;
		for (int i=0;i<L;i++){
			logWln(X[i]+" ");
		}
		log("");
	}
	static void log(Object[] X){
		int L=X.length;
		for (int i=0;i<L;i++){
			logWln(X[i]+" ");
		}
		log("");
	}


	static void log(Object o){
		logWln(o+"\n");
	}

	static void logWln(Object o){
		System.err.print(o);
		//	outputWln(o);

	}
	static void info(Object o){
		System.out.println(o);
		//output(o);
	}

	static void output(Object o){

		outputWln(""+o+"\n");

	}

	static void outputWln(Object o){
		// System.out.print(o);

		try {
			out.write(""+ o);
		} catch (Exception e) {

		}
	}

	static int pgcd(int a,int b){
		if (a<b)
			return pgcd(b,a);
		while (b!=0){
			int c=b;
			b=a%b;
			a=c;
		}
		return a;
	}


	// Global vars
	static BufferedWriter out;
	static InputReader reader;

	static long MOD=1000000007;


	static void process() throws Exception {



		out = new BufferedWriter(new OutputStreamWriter(System.out));
		reader=new InputReader(System.in);


		int n=reader.readInt();
		int p=0;
		boolean lastNeed=false;
		int res=0;
		for (int i=0;i<n+1;i++){
			int x;
			if (i<n) {
				x=reader.readInt();
				p=pgcd(x,p);
			} else
				x=2;
			if (x%2==1) {
				if (lastNeed){
					res++;
					lastNeed=false;
				} else {
					lastNeed=true;
				}
			} else {
				if (lastNeed){
					res+=2;
					lastNeed=false;
				}
			}
					
	
		}
		//log("p:"+p);
		String bob="YES";
		if (n==1){
			if (p==1)
				bob="NO";
		} else {
			if (p>1)
				res=0;
		}
			
		output(bob);
		if (bob.equals("YES"))
			output(res);

		try {
			out.close();
		}
		catch (Exception e){}


	}


	public static void main(String[] args) throws Exception {
		process();

	}

	static final class InputReader {
		private final InputStream stream;
		private final byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		private int read() throws IOException {
			if (curChar >= numChars) {
				curChar = 0;
				numChars = stream.read(buf);
				if (numChars <= 0) {
					return -1;
				}
			}
			return buf[curChar++];
		}


		public final String readString() throws IOException {
			int c = read();
			while (isSpaceChar(c)) {
				c = read();
			}
			StringBuilder res=new StringBuilder();
			do {
				res.append((char)c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public final int readInt() throws IOException {
			int c = read();
			boolean neg=false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d=(char)c;
			//log("d:"+d);
			if (d=='-') {
				neg=true;
				c = read();
			}
			int res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			//log("res:"+res);
			if (neg)
				return -res;
			return res;

		}

		public final long readLong() throws IOException {
			int c = read();
			boolean neg=false;
			while (isSpaceChar(c)) {
				c = read();
			}
			char d=(char)c;
			//log("d:"+d);
			if (d=='-') {
				neg=true;
				c = read();
			}
			long res = 0;
			do {
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			//log("res:"+res);
			if (neg)
				return -res;
			return res;

		}




		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
	}


}