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. . Mike wants to change his sequence in order to make it beautiful. In one move he can choose an index i (1 \le i \lt 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. is the biggest non-negative number d such that d divides bi for every i (1 \le i \le n).

Input The first line contains a single integer n (2 \le n \le 100000) - length of sequence A.The second line contains n space-separated integers a1,a2,...,an (1 \le ai \le 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.

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.