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 math

length=int(input())
inp=input().split()

seq=[]
for i in inp:
    seq+=[int(i)]

#print(seq)
if len(seq)!=length:
    raise Exception('wrong input')

def gcd_of(a, b):
    if b==0:
        return a
    else:
        q=math.floor(a/b)
        r=a-(q*b)
        return(gcd_of(b, r))

gcd=0
for number in seq:
    gcd=gcd_of(number,gcd)

if gcd!=-1 and gcd!=1:
    print('YES')
    print(0)
else:
    odd=0
    for i in seq:
        if i%2==1:
            odd+=1
        else:
            if odd%2==1:
                odd+=3

    if odd%2==1:
        odd+=3
    move_cnt=int(odd/2)

    print('YES')
    print(move_cnt)
