Mike and gcd problem - Problem

Mike has a sequence A=[a₁,a₂,...,a_n] of length n. He considers the sequence B=[b₁,b₂,...,b_n] beautiful if the gcd of all its elements is bigger than 1, i.e. $\text{[math]}$ .

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 a_i,a_i+1 and put numbers a_i-a_i+1,a_i+a_i+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.

$\text{[math]}$ is the biggest non-negative number d such that d divides b_i for every i (1≤i≤n).

Input

The first line contains a single integer n (2≤n≤100000) − length of sequence A.

The second line contains n space-separated integers a₁,a₂,...,a_n (1≤a_i≤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 $\text{[math]}$ .

In the second example the gcd of the sequence is already greater than 1.

1680: Mike and gcd problem

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