B'Bogocubic is playing a game with amenotiomoi. First, Bogocubic fixed an integer n , and then he gave amenotiomoi an integer x which is initially equal to 1 . In one move amenotiomoi performs one of the following operations with the same probability: Bogocubic wants to find the expected number of moves amenotiomoi has to do to make x greater than or equal to n . Help him find this number modulo 998 ,244 ,353 . Formally, let M = 998 ,244 ,353 . It can be shown that the answer can be expressed as an irreducible fraction frac{p}{q} , where p and q are integers and q not equiv 0 pmod{M} . Output the integer equal to p cdot q^{-1} bmod M . In other words, output such an integer y that 0 <= y < M and y cdot q equiv p pmod{M} . Each test contains multiple test cases. The first line contains the number of test cases t ( 1 <= t <= 100 ). The description of the test cases follows. The only line of each test case contains one integer n ( 1 <= n <= 10^{18} ). For each test case, output a single integer -- the expected number of moves modulo 998 ,244 ,353 . In the first test case, n <= x without any operations, so the answer is 0 . In the second test case, for n = 4 , here is the list of all possible sequences of operations and their probabilities: So the expected number of moves is 4 cdot <= ft(3 cdot frac{1}{8} right) + 2 cdot <= ft(2 cdot frac{1}{4} right) = frac{5}{2} equiv 499122179 pmod{998244353} . In the third test case, for n = 8 , the expected number of moves is frac{137}{32} equiv 717488133 pmod{998244353} . In the fourth test case, for n = 15 , the expected number of moves is frac{24977}{4096} equiv 900515847 pmod{998244353} . '...