± Increasing Sequence

AtCoder

IDarc153_c

Time2000ms

Memory256MB

Difficulty—

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: $N$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

5
-1 1 -1 -1 1

Output #1

Yes
-3 -1 4 5 7

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

Input #2

1
-1

Output #2

Yes
0

Input #3

2
1 -1

Output #3

No

API Response (JSON)

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    "name": "± Increasing Sequence",
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