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. 
def gcd(a,b):
    if a*b==0:
        return a+b
    if a<b:
        a,b=b,a
    if a%b==0:
        return b
    else:
        return gcd(b,a%b)
n=int(raw_input())
l=[0]+list(map(int,raw_input().split()))
dp=[0 for i in range(n+1)]
g=0
f=0
for i in range(1,n+1):
    g=gcd(g,l[i])
    if g==1:
        f=1
        break
print "YES"
if f==0:
    print 0
else:
    for i in range(1,n+1):
        if l[i]%2==0:
            dp[i]=dp[i-1]
        elif l[i-1]%2==0:
            dp[i]=dp[i-1]+2
        else:
            dp[i]=dp[i-2]+1
    print dp[n]
        

        
