For positive integers (i) and (j), define (f_i(j)) as the maximum integer (k) such that (i^k) divides (j). A number (j) is considered special if (f_6(j) \gt f_7(j)). For example, (6) is special , but (67) and (7) are not. You are given an array (a) of (n) positive integers. In one operation, you must increase every element in the array by (1). Your task is to find the minimum number of operations needed to make all elements in (a) special at the same time, or determine that it is impossible. The first line contains an integer (t) ((1 \leq t \leq 10^4)), the number of test cases. For each test case, the first line contains an integer (n) ((1 \leq n \leq 2 \cdot 10^5)). The second line of each test case contains (n) integers (a_1, a_2, \dots, a_n) ((1 \leq a_i \leq 10^9)). The sum of (n) over all test cases does not exceed (2 \cdot 10^5). For each test case, output a single integer: the minimum number of operations to make all elements special at the same time, or (-1) if it is impossible. In the first test case, all elements cannot be made special at the same time. In the second test case, performing (5) operations results in the array (30,72), whose elements are all special. In the fourth test case, the array becomes (9557358) after (7) operations.