{"trustable":true,"sections":[{"title":"","value":{"format":"MD","content":"Bamboo Pole-vault is a massively popular sport in Xzhiland. And Master Phi-shoe is a very popular coach for his success. He needs some bamboos for his students, so he asked his assistant Bi-Shoe to go to the market and buy them. Plenty of Bamboos of all possible integer lengths (yes!) are available in the market. According to Xzhila tradition,\n\nScore of a bamboo \u003d **\u0026Phi; (bamboo\u0027s length)**\n\n(Xzhilans are really fond of number theory). For your information, **\u0026Phi; (n)** \u003d numbers less than **n** which are relatively prime (having no common divisor other than 1) to **n**. So, score of a bamboo of length 9 is 6 as 1, 2, 4, 5, 7, 8 are relatively prime to 9.\n\nThe assistant Bi-shoe has to buy one bamboo for each student. As a twist, each pole-vault student of Phi-shoe has a lucky number. Bi-shoe wants to buy bamboos such that each of them gets a bamboo with a score greater than or equal to his/her lucky number. Bi-shoe wants to minimize the total amount of money spent for buying the bamboos. One unit of bamboo costs 1 `Xukha`. Help him."}},{"title":"Input","value":{"format":"MD","content":"Input starts with an integer **T (\u0026le; 100)**, denoting the number of test cases.\n\nEach case starts with a line containing an integer **n (1 \u0026le; n \u0026le; 10000)** denoting the number of students of Phi-shoe. The next line contains **n** space separated integers denoting the lucky numbers for the students. Each lucky number will lie in the range **[1, 10\u003csup\u003e6\u003c/sup\u003e]**."}},{"title":"Output","value":{"format":"MD","content":"For each case, print the case number and the minimum possible money spent for buying the bamboos. See the samples for details."}},{"title":"Sample","value":{"format":"HTML","content":"\u003ctable class\u003d\u0027vjudge_sample\u0027\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\n5\n1 2 3 4 5\n6\n10 11 12 13 14 15\n2\n1 1\n\u003c/pre\u003e\u003c/td\u003e\n \u003ctd\u003e\u003cpre\u003eCase 1: 22 Xukha\nCase 2: 88 Xukha\nCase 3: 4 Xukha\n\u003c/pre\u003e\u003c/td\u003e\n \u003c/tr\u003e\n\u003c/tbody\u003e\n\u003c/table\u003e\n"}}]}