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. 
from math import *
def prim (a):
    a=abs(a)
    if (a==1):
        return(False)
    else:
        j=2
        while(a%j!=0 and j<=sqrt(a)):
            j=j+1
        if(j>sqrt(a)):
            return(True)
        else:
            return(False)
def oszto (a,t):
    j=0
    while(j<len(t) and t[j]%a==0):
        j=j+1
    if (j==len(t)):
        return(True)
    else:
        return(False)
n=int(input())
s=input()
t=s.split()
for i in range (n):
    t[i]=int(t[i])
print("Yes")
k=sorted(t)[0]
i=2
while(i<=k):
    if(oszto(i,t)):
        break
    else:
        i=i+1
if(i<=k):
    print(0)
else:
    i=0
    csere=0
    while(i<n-1):
        if(t[i]%2==1 and t[i+1]%2==1):
            csere=csere+1
            t[i]=0
            t[i+1]=0
        if(t[i]%2==1 and t[i+1]%2==0):
            csere=csere+2
            t[i]=0
        i=i+1
    if(t[n-1]%2==1):
        csere=csere+2
    print(csere)
        
