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

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.

Constraints

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

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

见题面 Input 部分

见题面 Output 部分