{"trustable":true,"prependHtml":"\u003cstyle type\u003d\"text/css\"\u003e\n #problem-body \u003e pre {\n display: block;\n padding: 9.5px;\n margin: 0 0 10px;\n font-size: 13px;\n line-height: 1.42857143;\n word-break: break-all;\n word-wrap: break-word;\n color: #333;\n background: rgba(255, 255, 255, 0.5);\n border: 1px solid #ccc;\n border-radius: 6px;\n }\n\u003c/style\u003e\n","sections":[{"title":"","value":{"format":"HTML","content":"\u003cdiv id\u003d\"problem-body\"\u003e\n\t\u003cp\u003eGiven a string, you keep swapping any two characters in the string randomly till the string becomes a palindrome. What is the expected number of swaps you will make?\u003c/p\u003e\r\n\r\n\u003ch3\u003eInput\u003c/h3\u003e\r\n\u003cp\u003eThe first line contains the number of test cases T. Each of the next T lines contains a string each.\u003c/p\u003e\r\n\r\n\u003ch3\u003eOutput\u003c/h3\u003e\r\n\u003cp\u003eOutput T lines containing the answer for the corresponding test case. Print the answer rounded to exactly 4 decimal places.\u003c/p\u003e\r\n\r\n\u003ch3\u003eConstraints:\u003c/h3\u003e\r\n\u003cp\u003eT \u0026lt;\u003d 10000\u003c/p\u003e\r\n\u003cp\u003eThe length of the string will be at most 8 characters.\u003c/p\u003e\r\n\u003cp\u003eThe string will consist of only lower-case letters \u0027a\u0027-\u0027z\u0027.\u003c/p\u003e\r\n\u003cp\u003eThere will always be at least one palindrome which can be formed with the letters of the given string.\u003c/p\u003e\r\n\r\n\u003ch3\u003eSample\u003c/h3\u003e\r\n\u003cdiv\u003e\u003ctable class\u003d\"vjudge_sample\"\u003e\n\u003cthead\u003e\n \u003ctr\u003e\n \u003cth\u003eInput\u003c/th\u003e\n \u003cth\u003eOutput\u003c/th\u003e\n \u003c/tr\u003e\n\u003c/thead\u003e\n\u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd\u003e\u003cpre\u003e4\r\nb\r\nbb\r\nabb\r\ncbaabbb\r\n\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003e0.0000\r\n0.0000\r\n3.0000\r\n59.3380\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\r\n\r\n\u003ch3\u003eExplanation\u003c/h3\u003e\r\n\u003cp\u003eFor the first two cases, the string is already a palindrome so no swaps are needed.\u003c/p\u003e\r\n\u003cp\u003eFor the third case, there are 3 possible swaps. The string will become \"bab\",\"bba\" or remain \"abb\" with 1/3rd probability each. It\u0027s easy to see that the expected number of swaps needed is 3.0000\u003c/p\u003e\r\n\u003cp\u003eFor the last case, the answer is 59.337962..., which should be printed as 59.3380\u003c/p\u003e\r\n\n\u003c/div\u003e"}}]}