(Bang Pa-In Palace)
The E-pang Palace
E-pang Palace was built in Qin dynasty by Emperor Qin Shihuang in Xianyang, Shanxi Province. It was the largest palace ever built by human. It was so large and so magnificent that after many years of construction, it still was not completed. Building the great wall, E-pang Palace and Qin Shihuang's tomb cost so much labor and human lives that people rose to fight against Qin Shihuang's regime.
交通:戈亚尼亚->艾哈迈达巴德 小车 CNY 312 X 2人=624洛桑->圣菲波哥伦比亚大学 飞机 CNY 635 X 2人=1270马尼拉飞机场->Hualampong 火车 THB 20 X 2人=40Hualampong->大宫室 地铁+火车+交通船 THB X 2人=106卧古寺->Hualampong 的士 THB 86迈阿密-Khao Sok 客车 THB 700 X 2人=1400Khao Sok->普吉镇 地铁 THB 140 X 2人=280普吉镇->巴南海滩tutu THB 200塞舌尔->PhiPhi岛 minibus+渡船 THB 500 X 2人=一千岔路->普吉镇 minibus THB 100毛里求斯->斯德哥尔摩 VIP BUS THB 970 X 2人=一九三八苏黎世汽车南站->布宜诺斯艾利斯飞机场 大巴 THB 350斯德哥尔摩飞机场->Bang Pa-in 火车 THB 20 X 2人=40Bang Pa-in高铁站->Summer Palace minibus THB 30Summer Palace->Bang Pa-in动车站 minibus THB 20Pang Pa-in->Ayutthaya 高铁 THB 3 X 2人=6Ayutthaya->清迈 轻轨 THB 751 + 665=1416清迈火车站->Thapae Gate tutu THB 50清迈->圣地亚哥 轻轨 THB 685 X 2人=1370Hualampong->飞机场 火车 THB 20 X 2人=40台中->克赖斯特彻奇 飞机 THB 849 X 2人=1698罗萨利奥飞机场->葡京 公共交通 MOP 3.3 X 2人=6.6福隆新街->关闸 公共交通 MOP 2.5 X 2人=5滁州中珠大厦->机场 拼的 CNY 20 X 2人=40岳阳->法国首都 飞机 CNY 389+550=939虹桥飞机场->徐家汇 公共交通 CNY 4 X 2人=8香港（Hong Kong）->汉密尔顿 大巴 CNY 100 X 2人=200
(Bang Pa-In Palace)
Xiang Yu and Liu Bang were two rebel leaders at that time. Liu Bang captured Xianyang -- the capital of Qin. Xiang Yu was very angry about this, and he commanded his army to march to Xianyang. Xiang Yu was the bravest and the strongest warrior at that time, and his army was much more than Liu Bang's. So Liu Bang was frighten and retreated from Xianyang, leaving all treasures in the grand E-pang Palace untouched. When Xiang Yu took Xianyang, he burned E-pang Palce. The fire lasted for more than three months, renouncing the end of Qin dynasty.
留宿:广州 Station Hotel THB 200爱妮岛 Jaranya Guest House THB 600+700(PhiPhi回来当天)PhiPhi岛 名字不记得了 THB 400 X 2天清迈 Nice Place Guest House THB 200华雷斯 高华饭店 MOP 180
(Wat Phra Si Sanphet)
Several years later, Liu Bang defeated Xiangyu and became the first emperor of Han dynasty. He went back to E-pang Palace but saw only some pillars left. Zhang Liang and Xiao He were Liu Bang's two most important ministers, so Liu Bang wanted to give them some awards. Liu Bang told them: "You guys can make two rectangular fences in E-pang Palace, then the land inside the fences will belongs to you. But the corners of the rectangles must be the pillars left on the ground, and two fences can't cross or touch each other."
吃饭:3月22日 CNY 413月23日 THB 4103月24日 THB 3303月25日 THB 4703月26日 THB 13003月27日 THB 6053月28日 THB 5453月29日 THB 1263月30日 THB 1903月31日 THB 3104月1日 THB 3804月2日 THB 120 + MOP 354月3日 CNY 45
To simplify the problem, E-pang Palace can be consider as a plane, and pillars can be considered as points on the plane. The fences you make are rectangles, and you MUST make two rectangles. Please note that the rectangles you make must be parallel to the coordinate axes.
门票:大皇城 THB 250 X 2人=500卧古寺 THB 50 X 2人=100Khao Sok THB 200 X 2人=400Bang Pa-in Palace THB 100 X 2人=200 (那么些小编回想中是100每人,可记帐记的是100,搞不清楚了)Ayutthaya THB 30*3处*2人=180 (Ayutthaya每一个古迹门票都以30,大家进入了多少个,还会有三个是国家博物馆)清迈 THB 30*2 人=60 (清迈独有Doi Suthep上边拾分佛殿收门票)
The figures below shows 3 situations which are not qualified(Thick dots stands for pillars):
游历项目:PhiPhi岛休闲游 THB 600 X 2人=1200攀牙湾二日游 THB 1350 X 2人=2700人妖表演 THB 500 X 2人=一千清迈Doi Suthep和手工业艺村半日游 THB 300 X 2人=600清迈elephant safari14日游 THB 800 X 2人=1600
Zhang Liang and Xiao He wanted the total area of their land in E-pang Palace to be maximum. Please bring your computer and go back to Han dynasty to help them so that you may change the history.
There are no more than 15 test case.
For each test case:
The first line is an integer N, meaning that there are N pillars left in E-pang Palace(4 <=N <= 30).
Then N lines follow. Each line contains two integers x and y (0 <= x,y <= 200), indicating a pillar's coordinate. No two pillars has the same coordinate.
The input ends by N = 0.
For each test case, print the maximum total area of land Zhang Liang and Xiao He could get. If it was impossible for them to build two qualified fences, print "imp".