You are given a sequence of length $N$, $A = (A_1, \ldots, A_N)$, consisting of $1$ and $-1$. Determine whether there is an integer sequence $x = (x_1, \ldots, x_N)$ that satisfies all of the following conditions, and print one such sequence if it exists. - $|x_i| \leq 10^{12}$ for every $i$ ($1\leq i\leq N$). - $x$ is strictly increasing. That is, $x_1 < \cdots < x_N$. - $\sum_{i=1}^N A_ix_i = 0$.

The input is given from Standard Input in the following format: >$N$ $A_1$ $\ldots$ $A_N$ #### Constraints - $1\leq N\leq 2\times 10^5$ - $A_i \in \lbrace 1, -1\rbrace$

If there is an integer sequence $x$ that satisfies all of the conditions in question, print `Yes`; otherwise, print `No`. In case of `Yes`, print the elements of such an integer sequence $x$ in the subsequent line, separated by spaces. > $x_1$ $\ldots$ $x_N$ If multiple integer sequences satisfy the conditions, you may print any of them.