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문제

정찰 부대가 지금 막 새로운 보고를 보내왔습니다. 그 보고의 내용은 바로, ABCD(Atomic Beryllium-Cesium Destroyer)라는, 이름만 들어도 소름이 끼치는 병기가 테러리스트들에게 넘어갔다는 것입니다. ABCD는 무한히 길고 평행한 네 개의 거대한 레일로 이루어져 있으며, 각각의 레일에 부품이 하나씩 놓여있습니다. 우리가 ABCD의 부품을 하나라도 파괴하거나 레일에서 꺼내려고 하면 바로 ABCD가 작동할 것이고, 전세계를 아우르는 대재앙이 발생하게 됩니다. 테러리스트도 이러한 ABCD의 특징을 알고 있기 때문에, 굳이 이 장비를 보호하려고 하지도 않습니다. 아아, 인류는 이렇게 멸망하게 되는 걸까요?

하지만, 당신에게는 ABCD의 개발자에게 얻은 1급 기밀 정보가 있습니다! ABCD의 각각의 부품은 어린 아이도 들 수 있을 만큼 가벼워서, 레일 위에서 움직이는 것은 쉽습니다. 각각의 부품을 잘 움직여서, 만약 ABCD가 작동하려고 하는 순간 ABCD의 각각의 부품이 완벽하게 직사각형을 이루고 있다면, ABCD는 강한 방사능을 방출하면서, 스스로 기능을 잃고 자폭을 하게 됩니다. 정상적으로 작동하여 재앙이 발생하는 것보다야 훨씬 낫지만, 자폭을 시킬 수 있다면 그 때 발생하는 방사능으로 인한 피해 또한 줄이고 싶습니다. 방사능의 양은 ABCD가 이루는 직사각형의 넓이에 비례합니다.

당신은 ABCD로 인한 피해를 최소화하여, 궁극적으로 인류를 테러로부터 구해야 합니다!

입력

첫 번째 줄에는 10,000 이하의 양의 실수 p, q, r이 주어집니다. 이는 각각 레일 A와 B, B와 C, C와 D 사이의 거리에 해당합니다.

p, q, r은 소수점 이하 최대 두 자리까지 주어집니다.

출력

만일 ABCD를 자폭시킬 수 없어 인류가 비극적인 결말을 맞이할 수밖에 없다면 0을 출력합니다.

만일 ABCD를 자폭시킬 수 있다면, 자폭 시 ABCD가 이루는 직사각형의 최소 넓이를 소수점 넷째 자리까지 출력하세요.

예제 입력 1

3 2.0 3.00

예제 출력 1

30.0000

힌트

[{"problem_id":"3199","problem_lang":"0","title":"ABCD","description":"<p>\uc815\ucc30 \ubd80\ub300\uac00 \uc9c0\uae08 \ub9c9 \uc0c8\ub85c\uc6b4 \ubcf4\uace0\ub97c \ubcf4\ub0b4\uc654\uc2b5\ub2c8\ub2e4. \uadf8 \ubcf4\uace0\uc758 \ub0b4\uc6a9\uc740 \ubc14\ub85c, ABCD(Atomic Beryllium-Cesium Destroyer)\ub77c\ub294, \uc774\ub984\ub9cc \ub4e4\uc5b4\ub3c4 \uc18c\ub984\uc774 \ub07c\uce58\ub294 \ubcd1\uae30\uac00 \ud14c\ub7ec\ub9ac\uc2a4\ud2b8\ub4e4\uc5d0\uac8c \ub118\uc5b4\uac14\ub2e4\ub294 \uac83\uc785\ub2c8\ub2e4. ABCD\ub294 \ubb34\ud55c\ud788 \uae38\uace0 \ud3c9\ud589\ud55c \ub124 \uac1c\uc758 \uac70\ub300\ud55c \ub808\uc77c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uc73c\uba70, \uac01\uac01\uc758 \ub808\uc77c\uc5d0 \ubd80\ud488\uc774 \ud558\ub098\uc529 \ub193\uc5ec\uc788\uc2b5\ub2c8\ub2e4. \uc6b0\ub9ac\uac00 ABCD\uc758 \ubd80\ud488\uc744 \ud558\ub098\ub77c\ub3c4 \ud30c\uad34\ud558\uac70\ub098 \ub808\uc77c\uc5d0\uc11c \uaebc\ub0b4\ub824\uace0 \ud558\uba74 \ubc14\ub85c ABCD\uac00 \uc791\ub3d9\ud560 \uac83\uc774\uace0, \uc804\uc138\uacc4\ub97c \uc544\uc6b0\ub974\ub294 \ub300\uc7ac\uc559\uc774 \ubc1c\uc0dd\ud558\uac8c \ub429\ub2c8\ub2e4. \ud14c\ub7ec\ub9ac\uc2a4\ud2b8\ub3c4&nbsp;\uc774\ub7ec\ud55c ABCD\uc758 \ud2b9\uc9d5\uc744 \uc54c\uace0 \uc788\uae30 \ub54c\ubb38\uc5d0, \uad73\uc774 \uc774 \uc7a5\ube44\ub97c \ubcf4\ud638\ud558\ub824\uace0 \ud558\uc9c0\ub3c4 \uc54a\uc2b5\ub2c8\ub2e4. \uc544\uc544, \uc778\ub958\ub294 \uc774\ub807\uac8c \uba78\ub9dd\ud558\uac8c \ub418\ub294 \uac78\uae4c\uc694?<\/p>\r\n\r\n<p>\ud558\uc9c0\ub9cc, \ub2f9\uc2e0\uc5d0\uac8c\ub294 ABCD\uc758 \uac1c\ubc1c\uc790\uc5d0\uac8c \uc5bb\uc740 1\uae09 \uae30\ubc00 \uc815\ubcf4\uac00 \uc788\uc2b5\ub2c8\ub2e4! ABCD\uc758 \uac01\uac01\uc758 \ubd80\ud488\uc740 \uc5b4\ub9b0 \uc544\uc774\ub3c4 \ub4e4 \uc218 \uc788\uc744 \ub9cc\ud07c \uac00\ubcbc\uc6cc\uc11c, \ub808\uc77c \uc704\uc5d0\uc11c \uc6c0\uc9c1\uc774\ub294 \uac83\uc740 \uc27d\uc2b5\ub2c8\ub2e4. \uac01\uac01\uc758 \ubd80\ud488\uc744 \uc798 \uc6c0\uc9c1\uc5ec\uc11c, \ub9cc\uc57d ABCD\uac00 \uc791\ub3d9\ud558\ub824\uace0 \ud558\ub294 \uc21c\uac04 ABCD\uc758 \uac01\uac01\uc758 \ubd80\ud488\uc774 \uc644\ubcbd\ud558\uac8c \uc9c1\uc0ac\uac01\ud615\uc744 \uc774\ub8e8\uace0 \uc788\ub2e4\uba74, ABCD\ub294 \uac15\ud55c \ubc29\uc0ac\ub2a5\uc744 \ubc29\ucd9c\ud558\uba74\uc11c, \uc2a4\uc2a4\ub85c \uae30\ub2a5\uc744 \uc783\uace0 \uc790\ud3ed\uc744 \ud558\uac8c \ub429\ub2c8\ub2e4. \uc815\uc0c1\uc801\uc73c\ub85c \uc791\ub3d9\ud558\uc5ec \uc7ac\uc559\uc774 \ubc1c\uc0dd\ud558\ub294 \uac83\ubcf4\ub2e4\uc57c \ud6e8\uc52c \ub0ab\uc9c0\ub9cc, \uc790\ud3ed\uc744 \uc2dc\ud0ac \uc218 \uc788\ub2e4\uba74 \uadf8 \ub54c \ubc1c\uc0dd\ud558\ub294 \ubc29\uc0ac\ub2a5\uc73c\ub85c \uc778\ud55c \ud53c\ud574 \ub610\ud55c \uc904\uc774\uace0 \uc2f6\uc2b5\ub2c8\ub2e4. \ubc29\uc0ac\ub2a5\uc758 \uc591\uc740 ABCD\uac00 \uc774\ub8e8\ub294 \uc9c1\uc0ac\uac01\ud615\uc758 \ub113\uc774\uc5d0 \ube44\ub840\ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\ub2f9\uc2e0\uc740 ABCD\ub85c \uc778\ud55c \ud53c\ud574\ub97c \ucd5c\uc18c\ud654\ud558\uc5ec, \uad81\uadf9\uc801\uc73c\ub85c \uc778\ub958\ub97c \ud14c\ub7ec\ub85c\ubd80\ud130 \uad6c\ud574\uc57c \ud569\ub2c8\ub2e4!<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 10,000 \uc774\ud558\uc758 \uc591\uc758 \uc2e4\uc218 p, q, r\uc774 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \uc774\ub294 \uac01\uac01 \ub808\uc77c A\uc640 B, B\uc640 C, C\uc640 D \uc0ac\uc774\uc758 \uac70\ub9ac\uc5d0 \ud574\ub2f9\ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<p>p, q, r\uc740 \uc18c\uc218\uc810 \uc774\ud558 \ucd5c\ub300 \ub450 \uc790\ub9ac\uae4c\uc9c0 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4.<\/p>\r\n","output":"<p>\ub9cc\uc77c ABCD\ub97c \uc790\ud3ed\uc2dc\ud0ac \uc218 \uc5c6\uc5b4 \uc778\ub958\uac00 \ube44\uadf9\uc801\uc778 \uacb0\ub9d0\uc744 \ub9de\uc774\ud560 \uc218\ubc16\uc5d0 \uc5c6\ub2e4\uba74 0\uc744 \ucd9c\ub825\ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\ub9cc\uc77c ABCD\ub97c \uc790\ud3ed\uc2dc\ud0ac \uc218 \uc788\ub2e4\uba74, \uc790\ud3ed \uc2dc ABCD\uac00 \uc774\ub8e8\ub294 \uc9c1\uc0ac\uac01\ud615\uc758 \ucd5c\uc18c \ub113\uc774\ub97c \uc18c\uc218\uc810 \ub137\uc9f8 \uc790\ub9ac\uae4c\uc9c0 \ucd9c\ub825\ud558\uc138\uc694.<\/p>\r\n","hint":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/3199\/2.png\" style=\"height:225px; width:168px\" \/><\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"3199","problem_lang":"1","title":"ABCD","description":"<p><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/3199\/1.png\" style=\"float:left; height:189px; width:186px\" \/>A reconnaissance unit reports about an appliance found in the desert: the horrible weapon ABCD (Atomic Beryllium-Cesium Destroyer), fallen into terrorists&rsquo; hands. Its four components had been aligned there and in front and behind each of them a carrier rail spread &ldquo;beyond infinity&rdquo;, according to the report. Each attempt to destroy something and even to remove one of the parts from its rail would lead to global disaster. Terrorists know that and don&rsquo;t even make the effort to safeguard: they only wait for word of command to set the appliance going. The parts are not heavy, even a child could move them back and forth along their rails, which is harmless, but, alas, doesn&rsquo;t change their destructive power. Impasse!<\/p>\r\n\r\n<p>And yet! You have got some secret information from the developers of ABCD, which the terrorists do not know: if its four parts form a perfect rectangle at the moment of switching the weapon on, a self-destruction begins with the only consequence of high radiation in the frames of this rectangle. In comparison with the global catastrophe this may look like an insignificant damage, but it&rsquo;s a good idea to minimize it, too.<\/p>\r\n\r\n<p>And so, save the mankind! Write a program abcd to determine whether it is possible to rearrange the four parts along the rails in a way to form a perfect rectangle. If the answer is positive, calculate the minimal area possible which will inevitably be exposed to radiation by the process of self-destruction of ABCD. The necessary information is comprised in the report: the distances AB, BC and CD between the parallel rails (see the satellite snapshot above).<\/p>\r\n","input":"<p>One line is read from the standard input, containing three space separated positive real numbers: p=AB, q=BC and r=CD.<\/p>\r\n","output":"<p>Write one line to the standard output, containing:<\/p>\r\n\r\n<ul>\r\n\t<li>0, if no matter how A, B, C and D are moved each along its own rail, it is not possible to place them in a way to form an exactly perfect rectangle;<\/li>\r\n\t<li>one real number, formatted and rounded to the fourth decimal place: the area of the minimal rectangle, which can be obtained by moving the four parts, each along its own rail.<\/li>\r\n<\/ul>\r\n","hint":"<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/onlinejudgeimages.s3-ap-northeast-1.amazonaws.com\/problem\/3199\/2.png\" style=\"height:225px; width:168px\" \/><\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English","limit":"<p>The input numbers p, q and r are positive, not greater than 10000 measure units and with no more than 2 decimal digits.&nbsp;<\/p>\r\n"}]

출처

Olympiad > International Autumn Tournament in Informatics > 2010 > Group A (Seniors) 2번