{"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\u003eYou are given a set X \u003d {1, 2, 3, 4, …, 2n-1, 2n} where n is an integer. You have to find the number of interesting subsets of this set X.\u003c/p\u003e\r\n\u003cp\u003eA subset of set X is interesting if there are at least two integers a and b such that b is a multiple of a, i.e. remainder of b divides by a is zero and a is the smallest number in the set.\u003c/p\u003e\r\n\u003ch3\u003eInput\u003c/h3\u003e\r\n\u003cp\u003eThe input file contains multiple test cases. The first line of the input is an integer T (\u0026lt;\u003d 30) denoting the number of test cases. Each of the next T lines contains an integer \u0027n\u0027 where 1\u0026lt;\u003dn\u0026lt;\u003d1000.\u003c/p\u003e\r\n\u003ch3\u003eOutput\u003c/h3\u003e\r\n\u003cp\u003eFor each test case, you have to output as the format below:\u003c/p\u003e\r\n\u003cp\u003eCase X: Y\u0026nbsp;\u003c/p\u003e\r\n\u003cp\u003eHere X is the test case number and Y is the number of subsets. As the number Y can be very large, you need to output the number modulo 1000000007.\u003c/p\u003e\r\n\u003ch3\u003eExample\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\u003e3\r\n1\r\n2\r\n3\r\n\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase 1: 1\r\nCase 2: 9\r\nCase 3: 47\r\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n\u003c/div\u003e\n\u003c/div\u003e"}}]}