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 functools import reduce

def odd_count(arr):
	return sum(a % 2 for a in arr)

def count_moves(arr):
	return  odd_components(arr)

def odd_components(arr):
	parity = 0
	num_odd_components = 0
	odd_moves = 0
	odd_comp_size = 0
	for a in arr:
		parity = (parity + a)%2
		if a==1:
			odd_comp_size += 1
		if a==0:
			odd_moves += odd_comp_size//2 + 2*(odd_comp_size%2)
			odd_comp_size = 0

	odd_moves += odd_comp_size//2 + 2*(odd_comp_size%2)

	return odd_moves

def gdc(a, b):
	return b if a % b == 0 else gdc(b, a%b)

def array_gdc(arr):
	return reduce(gdc, arr)

seq_size = int(input())
A = [int(x) for x in input().split(' ')]

d = array_gdc(A)


if d > 1:
	print('YES\n0')
else:
	A = [a%2 for a in A]
	print('YES\n'+str(count_moves(A)))