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Задачи
1155. Hell on the Markets
Олимпиадные задачи на английском языке| 06/12/2008 | Занятие 10 (задачи NEERC 2008) (H) |
Ограничения: время – 1s/2s, память – 64MiB Ввод: input.txt или стандартный ввод Вывод: output.txt или стандартный вывод 
Послать решение Blockly Посылки Темы Где Обсудить (0)
Most financial institutions had become insolvent during financial crisis and went bankrupt or were bought
by larger institutions, usually by banks. By the end of financial crisis of all the financial institutions only
two banks still continue to operate. Financial markets had remained closed throughout the crisis and
now regulators are gradually opening them. To prevent speculation and to gradually ramp up trading
they will initially allow trading in only one financial instrument and the volume of trading will be limited
to `i` contracts for `i`-th minute of market operation.
Two banks had decided to cooperate with the government to kick-start the market operation. The boards
of directors had agreed on trading volume for each minute of this first trading session. One bank will
be buying ai contracts (`1\ ≤\ a_i\ ≤\ i`) during `i`-th minute (`1\ ≤\ i\ ≤\ n`), while the other one will be selling.
They do not really care whether to buy or to sell, and the outside observer will only see the volume `a_i`
of contracts traded per minute. However, they do not want to take any extra risk and want to have no
position in the contract by the end of the trading session. Thus, if we define `b_i\ =\ 1` when the first bank
is buying and `b_i\ =\ -1` when the second one is buying (and the first one is selling), then the requirement
for the trading session is that `sum_{i=1}^n\ a_i*b_i\ =\ 0`.
Your lucky team of three still works in the data center (due to the crisis, banks now share the data center
and its personnel) and your task is to find such `b_i` or to report that this is impossible.
Input
The first line of the input file contains the single integer number `n` (`1\ ≤\ n\ ≤\ 100\ 000`).
The second line of the input file contains `n` integer numbers – `a_i` (`1\ ≤\ a_i\ ≤\ i`).
Output
The first line of the output file must contain "Yes" if the trading session with specified volumes is possible
and "No" otherwise. In the former case the second line must contain `n` numbers – `b_i`.
Sample Input 1
4 1 2 3 4
Sample Output 1
Yes 1 -1 -1 1
Sample Input 2
4 1 2 3 3
Sample Output 2
No
