A10907. Mike and gcd problem

Mike has a sequence $A=[a_{1},a_{2},...,a_{n}]$ of length $n$ . He considers the sequence $B=[b_{1},b_{2},...,b_{n}]$ beautiful if the $gcd$ of all its elements is bigger than $1$ , i.e. .

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.

 is the biggest non-negative number $d$ such that $d$ divides $b_{i}$ for every $i$ ( $1<=i<=n$ ).

The first line contains a single integer $n$ ( $2<=n<=100000$ ) — length of sequence $A$ .

The second line contains $n$ space-separated integers $a_{1},a_{2},...,a_{n}$ ( $1<=a_{i}<=10^{9}$ ) — elements of sequence $A$ .

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.

In the first example you can simply make one move to obtain sequence $[0,2]$ with .

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