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.

Sample Input 1

5
-1 1 -1 -1 1

Sample Output 1

Yes
-3 -1 4 5 7

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

Sample Input 2

1
-1

Sample Output 2

Yes
0

Sample Input 3

2
1 -1

Sample Output 3

No