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 sys import stdin, stdout

def gcd(a,b):
    if a==0:
        return b
    elif b==0:
        return a
    elif a==b:
        return a
    else:
        while b:
            a, b = b, a%b
        return a
      
def seqGCD(a):
    currentGCD = gcd(a[0],a[1])
    i=2
    n=len(a)
    while currentGCD!=1 and i<n:
        currentGCD = gcd(currentGCD,a[i])
        i+=1
    return currentGCD
        
n = int(stdin.readline().rstrip())
a = stdin.readline().rstrip().split()
a = [int(b) for b in a]

if seqGCD(a)>1:
    print("YES")
    print(0)
else:
    moves=0
    i=0
    while i+1<n:
        if a[i]%2==0:
            i+=1
        elif a[i+1]%2==1:
            moves+=1
            i+=2
        else:
            moves+=2
            i+=2
    if i==n-1 and a[i]%2==1:
        moves+=2
    print("YES")
    print(moves)
