B'Serval loves playing music games. He meets a problem when playing music games, and he leaves it for you to solve. You are given n positive integers s_1 < s_2 < ldots < s_n . f(x) is defined as the number of i ( 1 <= q i <= q n ) that exist non-negative integers p_i, q_i such that: s_i=p_i <= ft lfloor{s_n over x} right rfloor + q_i <= ft lceil{s_n over x} right rceil Find out sum_{x=1}^{s_n} x cdot f(x) modulo 998 ,244 ,353 . As a reminder, lfloor x rfloor denotes the maximal integer that is no greater than x , and lceil x rceil denotes the minimal integer that is no less than x . Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= q t <= q 10^4 ). The description of the test cases follows. The first line of each test cases contains a single integer n ( 1 <= q n <= q 10^6 ). The second line of each test case contains n positive integers s_1,s_2, ldots,s_n ( 1 <= q s_1 < s_2 < ldots < s_n <= q 10^7 ). It is guaranteed that the sum of n over all test cases does not exceed 10^6 , and the sum of s_n does not exceed 10^7 . For each test case, print a single integer in a single line -- the sum of x cdot f(x) over all possible x modulo 998 ,244 ,353 . For the first test case, s_n=4 , f(x) are calculated as followings: Therefore, the answer is sum_{x=1}^4 x cdot f(x) = 1 cdot 1 + 2 cdot 2 + 3 cdot 3 + 4 cdot 3 = 26 . For the second test case: For example, when x=3 we have f(3)=1 because there exist p_4 and q_4 : 9 = 1 cdot <= ft lfloor{9 over 3} right rfloor + 2 cdot <= ft lceil{9 over 3} right rceil It can be shown that it is impossible to find p_1,p_2,p_3 and q_1,q_2,q_3 that satisfy the conditions. When x=5 we have f(5)=4 because there exist p_i and q_i as followings: 1 = 1 '...