A11648 | Is This a Zebra?

A camera you have accidentally left in a desert has taken an interesting photo. The photo has a resolution of $n$ pixels width, and each column of this photo is all white or all black. Thus, we can represent the photo as a sequence of $n$ zeros and ones, where $0$ means that the corresponding column is all white, and $1$ means that the corresponding column is black.

You think that this photo can contain a zebra. In this case the whole photo should consist of several (possibly, only one) alternating black and white stripes of equal width. For example, the photo $[0,0,0,1,1,1,0,0,0]$ can be a photo of zebra, while the photo $[0,0,0,1,1,1,1]$ can not, because the width of the black stripe is $3$ , while the width of the white stripe is $4$ . Can the given photo be a photo of zebra or not?

The first line contains a single integer $n$ ( $1<=n<=100000$ ) — the width of the photo.

The second line contains a sequence of integers $a_{1},a_{2},...,a_{n}$ ( $0<=a_{i}<=1$ ) — the description of the photo. If $a_{i}$ is zero, the $i$ -th column is all black. If $a_{i}$ is one, then the $i$ -th column is all white.

If the photo can be a photo of zebra, print "YES" (without quotes). Otherwise, print "NO".

You can print each letter in any case (upper or lower).