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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.*;
import java.math.*;


public class atcbg {
	//By shwetank_verma
	
    
	public static void main(String[] args) {
		FastReader sc = new FastReader();

		int t = 1;
		//t=sc.nextInt();

		while (t-- > 0) {
			int n=sc.nextInt();
			int a[]=new int[n];
			int g=0;
			for(int i=0;i<n;i++) {
				a[i]=sc.nextInt();
				g=gcd(g,a[i]);
			}
			System.out.println("YES");
			if(g>1) {
				
				System.out.println(0);
			}
			else {
				int c=0;
				for(int i=0;i<n;i++) {
					if(a[i]%2!=0) {
					if(i+1<n) {
						if(a[i+1]%2==0) {
							c+=2;
							a[i]^=1;
						}
						else {
							a[i]^=1;
							a[i+1]^=1;
							c++;
						}
					}
					else
						c+=2;
					}
				}
				System.out.println(c);
			}
		    
		}
		
		

	}
	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;
		}
	}

	static int mod = (int) (1e9 + 7);
	static boolean primes[] = new boolean[1000007];
	static ArrayList<Integer> b = new ArrayList<>();

	static void seive(int n) {
		Arrays.fill(primes, true);
		primes[0] = primes[1] = false;
		for (int i = 2; i * i <= n; i++) {
			if (primes[i] == true) {
				for (int p = i * i; p <= n; p += i) {
					primes[p] = false;
				}
			}
		}
		if (n < 1000007) {
			for (int i = 2; i <= n; i++) {
				if (primes[i])
					b.add(i);
			}

		}

	}

	static int gcd(int a, int b) {
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	static long GCD(long a, long b) {
		if (b == 0)
			return a;
		return GCD(b, a % b);
	}

	static long LCM(long a, long b) {
		return (a * b) / GCD(a, b);
	}

	static int lcm(int a, int b) {
		return (a * b) / gcd(a, b);
	}

	static ArrayList<Integer> segseive(int l, int r) {

		ArrayList<Integer> isprime = new ArrayList<Integer>();
		boolean p[] = new boolean[r - l + 1];
		Arrays.fill(p, true);

		for (int i = 0; b.get(i) * b.get(i) <= r; i++) {
			int currprime = b.get(i);
			int base = (l / currprime) * currprime;
			if (base < l) {
				base += currprime;
			}
			for (int j = base; j <= r; j += currprime) {
				p[j - l] = false;
			}

			if (base == currprime) {
				p[base - l] = true;
			}

		}
		for (int i = 0; i <= r - l; i++) {
			if (p[i])
				isprime.add(i + l);
		}
		return isprime;
	}

	static int LowerBound(long a[], long x) { // x is the target value or key
		int l = -1, r = a.length;
		while (l + 1 < r) {
			int m = (l + r) >>> 1;
			if (a[m] >= x)
				r = m;
			else
				l = m;
		}
		return r;
	}

	static int UpperBound(int a[], int x) {// x is the key or target value
		int l = -1, r = a.length;
		while (l + 1 < r) {
			int m = (l + r) >>> 1;
			if (a[m] <= x)
				l = m;
			else
				r = m;
		}
		return l + 1;
	}

	static void addEdge(ArrayList<ArrayList<Integer>> adj, int u, int v) {
		adj.get(u).add(v);
		adj.get(v).add(u);
	}

	static void BFS(ArrayList<ArrayList<Integer>> adj, int s, boolean visited[]) {
		Queue<Integer> q = new LinkedList<>();
		q.add(s);
		visited[s] = true;
		while (!q.isEmpty()) {
			int u = q.poll();
			for (int v : adj.get(u)) {
				if (!visited[v]) {
					visited[v] = !visited[v];
					q.add(v);
				}
			}
		}
	}

	static int BFSconnectedcount(ArrayList<ArrayList<Integer>> adj, int v) {
		boolean visited[] = new boolean[v + 1];
		int count = 0;
		for (int i = 0; i < v; i++) {
			if (!visited[i]) {
				BFS(adj, i, visited);
				count++;
			}
		}
		return count;
	}

	public static long power(long x, long y, long p) {
		long res = 1;
		x = x % p;
		while (y > 0) {
			if ((y & 1) == 1) {
				res = (res * x) % p;
			}
			y = y >> 1;
			x = (x * x) % p;
		}
		return res;
	}

	public static long monInverse(long n, long p) {
		return power(n, p - 2, p);
	}

	public static long nCrModPFermat(int n, int r, int p) {
		long[] fac = new long[n + 1];
		fac[0] = 1;
		for (int i = 0; i < n; i++) {
			fac[i + 1] = (fac[i] * (i + 1)) % p;
		}
		long x = monInverse(fac[r], p);
		long y = monInverse(fac[n - r], p);
		//System.out.println(fac[n]);
		return (((fac[n] * x) % p) * (y % p)) % p;
	}

	// This class implements 
	// Comparator interface
	static class Point implements Comparable<Point> {

		int x;
		int y;

		public Point(int x, int y) {
			this.x = x;
			this.y = y;
		}

		@Override
		public int compareTo(Point o) {

			return x - o.x;

		}
	}

	static int maxSubArraySum(int a[], int size) {
		int max_so_far = a[0];
		int curr_max = a[0];

		for (int i = 1; i < size; i++) {
			curr_max = Math.max(a[i], curr_max + a[i]);
			max_so_far = Math.max(max_so_far, curr_max);
		}
		return max_so_far;
	}

	static int maxsum(int a[], int n) {
		int s = 0;
		int res = 0;
		int sum[] = new int[n];
		sum[0] = a[0];
		for (int i = 1; i < n; i++) {
			sum[i] = sum[i - 1] + a[i];
		}
		for (int i = 0; i < n; i++) {
			s = Math.max(s, sum[i]);
		}
		return s;
	}

	static void leftRotate(int arr[], int d, int n) {
		for (int i = 0; i < d; i++)
			leftRotatebyOne(arr, n);
	}

	static void leftRotatebyOne(int arr[], int n) {
		int i, temp;
		temp = arr[0];
		for (i = 0; i < n - 1; i++)
			arr[i] = arr[i + 1];
		arr[i] = temp;
	}

	static boolean checkleapyear(long n) {
		if (((n % 4 == 0 && n % 100 != 0) || n % 400 == 0)) {
			return true;
		}
		return false;
	}

	static void DFS(ArrayList<ArrayList<Integer>> adj, int v, int s) {
		boolean visited[] = new boolean[v];
		DFSRec(adj, s, visited);
	}

	static void DFSRec(ArrayList<ArrayList<Integer>> adj, int s, boolean[] visited) {
		visited[s] = true;
		System.out.print(s + " ");
		for (int u : adj.get(s)) {
			if (!visited[u])
				DFSRec(adj, u, visited);
		}
	}

	

}

