To Win the Honor

Time Limit: 1 Second    Memory Limit: 32768 KB

July 1st, 2003. It was a fantastic day. Tonight, our National Football Team would challenge the Brazil in the final of the 2006 FIFA World Cup.

6:30, Berliner Olympiastadion, full of the stadium, seas of red and yellow. Fans were all clapping and cheering rhythmically for all of the players who were introduced to the crowd before kick-off, the scene was set for a wild 90 minutes.

With a whistle, both side began to play the game which was later described full of passion, drama and excitement.

Shao Jiayi, the best Midfield Commander all over the world, almost made an immediate impact after only 3 minutes. He beat three Brazil defenders before Gilberto Silva checked his run inside the box. However, referee Rob Styles waived away claims for a penalty.

Brazil was still the Brazil, in the twelfth minute Ronaldinho linked with Ronaldo. The Real Madrids attackers final searing shot fizzed past the upright. Eight minutes later the duo combined again to get into the area but the final pass from the creative midfielder was just beyond the Brazils striker.

After some great sweeping moves, Li Tie shot over the bar with his right foot from eight yards out at the end of a passing move initiated by Du Wei in defence.

China were in the ascendancy in the first half and headers from Li Weifeng and Du Wei sailed narrowly wide of the target.

In the twenty fourth minute, Yu Xing, a 21-year-old striker who was the Italy Serie A Top Goalscorer last year, came close to something of a wonder goal. He ran into the Brazil's defence from the halfway line and unleashed a terrific shot but it was just off target. For all their dominance China at times over elaborated in the final third and with all their possession should have been ahead. But it was Brazil who took the lead. Li Weifeng was booked for a foolish foul on Kaka in the 35 minutes. Kaka latched on to Roberto Carlos' pass that sent him clear of the China defence. Li Weifeng, who was tracking back, tried desperately to redeem the situation, but rudely brought the Brazil talent down in the area, earning him a yellow card. From the resulting penalty, Ronaldo blasted the ball home to give Brazil the lead.

The reds fell silent until Yu Xing completed a goal with a wonderful solo effort after 5 minute in which his immense talent shone so brightly. He ran from deep to draw the Brazil defence, beat 2 defenders and shot low to the left hand corner to equalize the score! The world-class goal send Olympiastadion wild! China were level!
The second half started in a crazy ambience. All of the 22 player did their best to break the deadlock. So tackling became more and more hard. Only after 3 minute, the China attacker Li Yi was on the wrong end of a clumsy challenge from Lucio, which left the fast attacker requiring a prolonged spell of treatment because of the recrudescence of his knee injury. Li Yi limped off the park, giving Qu Bo an earlier than expected taste of the action. The 25-year-old almost grabbed the deadlock-breaker seconds after coming on, but hooked his shot over the crossbar from 12-yards.

60th minute, Brazil nearly lead again. Sandrinho had a great opportunity to put the Yellows ahead when he raced on to Ronaldinho's through ball. However, the pacy striker fired straight at An Qis legs and the danger was cleared.

But alarm was not removed, after a goalmouth scramble 5 minutes later, Geovanni clipped the ball in off the post to drive Brazil supporters mad. The goals gave Brazil the impetus again to take control of the match and they once again dominated the play.

Time went by, situation seemed worse and worse to China. And then, miraculous things happened. 83th minute, Li Tie put in a cross field pass to Li Chunyu on the right hand side. The China U23 player held the ball up before a neat back pass into the path of Jihai Sun. The Chinese defender was brought down by Luiz Alberto and referee Rob Styles pointed to the spot!

Suddenly, the stadium became totally silence, contrasting clearly with the clamor just a moment ago. Everyone held breath. Yu Xing went up, put the ball on the spot. Deep breathe, step up, fire! The ball hit the crossbar then rebounded into the net just like a bullet! Dida was close to reaching the penalty, but sadly not close enough. All the Chinese players on the ground, Red supporters in the stadium, 1.1 thousand million people in China, suddenly burst out shouting! COME ON! CHINA! TO WIN THE HONOR!

Lack of stamina, none of the two teams had create effective attack in the added time and extra time. 2: 2, then enter the cruel Penalty Kick! As the Coach of the team, you need to choose the best five players from your team. Good Luck to you, and remember to Win the Honor!

Input

Input consists of several test cases. Each case will contain 11 lines. Each line refers to a player.

The input format is like this:

name shoot-power shoot-accuracy

where name is a string with length less than 50, the other two are all positive integers which are less than 20. For example, YuXing 19 19.
The input ends with the string "END".

A percentage of 1-(shoot-accuracy*5) of the player will shoot out off the target, and (shoot-accuracy*5)% will be on target. Shoot on target means each point inside the gate is equally likelyto be taken as the shoot point. The speed of the ball is shoot-power (m/s), and you can ignore the gravity.

The keeper stands on the ground, at middle of the gate, and can be assumed as a particle. As soon as the ball is kicked off, he jumps to the shoot point on the gate plane at a constant speed of 5 (m/s). If he reaches the point later than the ball does, it's a goal! Otherwise the ball would be caught. Therefore the gate plane is divided into Goal-area (Ga) and Lost-area (La).

You need to calculate the probability of a goal, that is, P=S(Ga)/(S(Ga)+S(La)), where of course, S(Ga)+S(La)=S(Gate). And more, please choose the players with the top 5 of the P's -- they are the best penalty kickers of the team. If two players' probabilities are equal, choose the alphabetically smaller name. Assume that there will never be two players with the same name.

A few tips of the football game:
> the height of the gate, H=2.5 (m);
> the width of the gate, W=7.5 (m);
> the distance from the penalty spot to the gate, D=11 (m).

Output

Output the best 5 player like this:

Case i:
name1 P1
name2 P2
......
name5 P5

where P1 >= P2 >= P3 >= P4 >= P5. Each Pi should be printed as a percentage which is accurate up to 2 decimal places. There must be a blank line after each case.

Sample Input

YuXing 19 19
ShaoJiayi 17 18
SunJihai 17 13
LiWeifeng 17 11
DuWei 18 15
LiChunyu 16 19
AnQi 18 2
LiTie 18 8
QoBo 16 17
ZhengZhi 17 16
XuLiang 15 19
END

Sample Output

Case 1:
YuXing 29.06%
DuWei 18.74%
ShaoJiayi 16.91%
ZhengZhi 15.03%
SunJihai 12.22%

Submit

Source: ZOJ Monthly, October 2003