Лимит времени 3000/4000/4000/4000 мс. Лимит памяти 65000/65000/65000/65000 Кб.
Автор: Фёдор Меньшиков, ВГПУ.
In ordinary lotteries odds to win a prize are proportional to the number of
bought lottery tickets. Organizers of a new lottery decided to encourage
participants of the lottery to buy as much as possible lottery tickets by
the fact that probability to win grows faster than the number of bought
lottery tickets, namely proportional to the square of the number of the
tickets bought by a participant.
There are three grand prizes in the lottery. Let's name them the first, the
second and the third ones. Drawing of the lottery takes place in the
following way. Stones are placed into a box. The number of stones
corresponding to each participant is equal to the square of the number of
the lottery tickets bought by that participant. Then stones are shuffled in
the box and the winning stone is picked out of the box. The stone
determines participant winning the first prize. Prior to the drawing of the
second and the third prizes all stones of the first prize winner are
removed from the box, so the first prize winner does not participate in the
drawing of the next prizes.
After removing of the stones of the first winner, stones in the box are
shuffled again, and again the winning stone is picked out of the box. The
stone determines participant winning the second prize. Prior to the drawing
of the last third prize all stones of the second prize winner are removed
from the box, so the first and the second prize winners do not participate
in the drawing of the third prize.
After removing of the stones of the second winner, stones in the box are
shuffled the last time and a stone determining participant getting the
third prize is picked out of the box. The drawing of the three grand prizes
complete.
If happens that all stones are taken out of the box (it is possible when
the number of participants of the lottery is less than 3) the remaining
prizes are not assigned to any participant.
In this problem you are given the number of the lottery tickets bought by
each of the lottery participant. You are to find the probability of winning
the first, the second and the third prize for each of the lottery participants.
Let's consider the computation of the probability using the following
example. There are 2 participants in the lottery, the participant A bought
2 lottery tickets and the participant B bought 1 lottery ticket.
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For the first prize drawing the box will contain 2x2=4 stones of the
participant A and 1x1=1 stone of the participant B, total 4+1=5 stones. The
probability of winning the first prize for each participant is equal to the
number of stones of that participant in the box divided by the total number
of stones in the box. For the participant A the probability is equal to 4/5
and for the participant B the probability is equal to 1/5. Because of small
number of the participants in this case the participant not winning the
first prize certainly gets the second prize. The probability to win the
second prize is 1/5 for the participant A and is 4/5 for the participant B.
Input
The first line of the input contains the number of the lottery participants
N which is integer from 0 to 256 inclusive. Each of the following N
lines contains the number of the lottery tickets boughts by a lottery participant
which is integer from 0 to 256 inclusive.
Output
The output should contain N lines. One line describe one lottery
participant. Each line should contain 3 fixed point numbers with exactly 3
digits after decimal point. Numbers should be separated by single spaces.
These numbers are the probabilities to win the first, the second and the
third prize for the participant.
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Input 1
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Output 1
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2
2
1
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0.800 0.200 0.000
0.200 0.800 0.000
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Для отправки решений необходимо выполнить вход.
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