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:
        return gcd(b,a)
    if a % b == 0:
        return b
    return gcd(b,a%b)
n = int(input())
a = list(map(int, input().split()))
k = gcd(a[0],a[1])
if n > 2:
    for i in a[2:]:
        k = gcd(k,i)
print('YES')
if k > 1:
    print(0)
else:
    s,t = 0,0
    for i in a:
        if i % 2 == 1:
            s += 1
        else:
            if s % 2 == 0:
                t += s//2
            else:
                t += s//2 + 2
            s = 0
    if s % 2 == 0:
        t += s//2
    else:
        t += s//2 + 2
    print(t)