Score : $600$ points

Problem Statement

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, $x_1 < \cdots < x_N$.
• $\sum_{i=1}^N A_ix_i = 0$.

Constraints

• $1\leq N\leq 2\times 10^5$
• $A_i \in \lbrace 1, -1\rbrace$

Input

The input is given from Standard Input in the following format:

$N$

$A_1$ $\ldots$ $A_N$

Output

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.

5
-1 1 -1 -1 1

Yes
-3 -1 4 5 7

For this output, we have $\sum_{i=1}^NA_ix_i= -(-3) + (-1) - 4 - 5 + 7 = 0$.

1
-1

Yes
0

2
1 -1

No