Ones

Let $x$ be a sequence of zeros and ones. An utterly forlorn one (UFO) in $x$ is an extreme one (either the first or the last one in the sequence) that additionally does not neighbour any other one. For example, the sequence $10001010$ has two UFOs, the sequence $1101011000$ has no UFO, and the sequence $1000$ has exactly one UFO.

Let $sks(n)$ denote the total number of UFOs in the binary representations of the numbers from $1$ to $n$. For example, $sks(5)=5$, $sks(64)=59$, $sks(128)=122$, and $sks(256)=249$.

We will work with very large numbers, so we represent them succinctly. Let $x$ be a positive integer and let $(x)_2$ be its binary representation, which starts with $1$. The succinct representation of $x$ is the sequence $REP(x)$ of positive integers giving the lengths of the successive maximal blocks of equal digits. For example:

$REP(460288) = REP(1110000011000000000_2) = (3, 5, 2, 9)$

$REP(408) = REP(110011000_2) = (2, 2, 2, 3)$

Given $REP(n)$, compute the sequence $REP(sks(n))$.

The first line contains one integer $k$ ($1 \le k \le 10^6$), the length of the succinct representation of a positive integer $n$. The second line contains $k$ integers $x_1, x_2, \ldots, x_k$ ($0 < x_i \le 10^9$) separated by single spaces; this sequence is the succinct representation of $n$. You may assume that $x_1 + x_2 + \cdots + x_k \le 10^9$, that is $0 < n < 2^{10^9}$.

Print two lines. The first line contains a single positive integer $l$. The second line contains $l$ positive integers $y_1, y_2, \ldots, y_l$ separated by single spaces, forming the succinct representation of $sks(n)$.