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 sys
input=sys.stdin.readline
import random
from collections import deque,defaultdict
L=lambda : list(map(int,input().split()))
Ls=lambda : list(input().split())
M=lambda : map(int,input().split())
I=lambda :int(input())
d=defaultdict(int)
import math as mt
n=I()
l=L()
g=0
c=0
for i in range(n):
    g=mt.gcd(g,l[i])
    if(l[i]%2==1):
        c+=1
if(g>1):
    print("YES")
    print(0)
else:
    a=0
    i=0
    f=0
    if(len(set(l))==1 and list(set(l))[0]==0 ):
            print("NO")
    else:
        while(i<n-1):
            if(l[i]%2==1 and l[i+1]%2==1):
                a+=1
                l[i]+=1
                l[i+1]+=1
                i+=2
            else:
                i+=1
        i=0
        while(i<n-1):
            if(l[i]%2==1 and l[i+1]%2==0):
                a+=2
                i+=2
            elif(l[i]%2==0 and l[i+1]%2==1):
                a+=2
                i+=2
            else:
                i+=2
        if(i==n-1 and l[i]%2==1):
            a+=2
        print("YES")
        print(a)
