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.*;

 
 
import java.util.*;
/*
 
 
 */


 
 
 
 
public class C {
    static FastReader sc=null;
    
    
	public static void main(String[] args) {
		sc=new FastReader();
		int n=sc.nextInt();
		int a[]=sc.readArray(n);
		int gcd=0;
		for(int e:a)gcd=gcd(e,gcd);
		if(gcd>1) {
			System.out.println("YES");
			System.out.println(0);
			return;
		}
		for(int i=0;i<n;i++)a[i]=a[i]%2;
		ArrayList<Integer> blocks=new ArrayList<>();
		int c=0;
		for(int i=0;i<n;i++) {
			c++;
			if(i==n-1 || a[i]!=a[i+1]) {
				if(blocks.isEmpty() && a[i]==0) {
					c=0;
					continue;
				}
				if(i==n-1 && a[i]==0) {
					c=0;
					continue;
				}
				blocks.add(c);
				c=0;
			}
		}
		n=blocks.size();
		//System.out.println(blocks.toString());
		int sum=0;
		for(int i=0;i<n;i+=2)sum+=(blocks.get(i)+1)/2 +(blocks.get(i)%2==1?1:0);
		System.out.println("YES");
		System.out.println(sum);
		
		
		
		
		
		
	}
	
	
    static void ruffleSort(int a[]) {
    	ArrayList<Integer> al=new ArrayList<>();
    	for(int i:a)al.add(i);
    	Collections.sort(al);
    	for(int i=0;i<a.length;i++)a[i]=al.get(i);
    }
    
    static void ruffleSort(long a[]) {
        ArrayList<Long> al=new ArrayList<>();
        for(long i:a)al.add(i);
        Collections.sort(al);
        for(int i=0;i<a.length;i++)a[i]=al.get(i);
    }
    
    static int[] reverse(int a[]) {
        ArrayList<Integer> al=new ArrayList<>();
        for(int i:a)al.add(i);
        Collections.sort(al,Collections.reverseOrder());
        for(int i=0;i<a.length;i++)a[i]=al.get(i);
        return a;
    }
 
    static int gcd(int a,int b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}  
    static long gcd(long a,long b) {
		if(b==0)return a;
		else return gcd(b,a%b);
	}  
        
 
    
    
    
    static void print(long a[]) {
        for(long e:a) {
            System.out.print(e+" ");
        }
        System.out.println();
    }
    static void print(char a[]) {
        for(char e:a) {
            System.out.print(e);
        }
        System.out.println();
    }
    
    
    static void print(int a[]) {
        for(int e:a) {
            System.out.print(e+" ");
        }
        System.out.println();
    }
    
    
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
        int[] readArray(int n) {
            int a[]=new int [n];
            for(int i=0;i<n;i++) {
                a[i]=sc.nextInt();
            }
            return a;
        }
        long[] readArrayL(int n) {
            long a[]=new long [n];
            for(int i=0;i<n;i++) {
                a[i]=sc.nextLong();
            }
            return a;
        }
    } 
}