B. Effects of Anti Pimplestime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputChaneka has an array [a_1,a_2,\ldots,a_n]. Initially, all elements are white. Chaneka will choose one or more different indices and colour the elements at those chosen indices black. Then, she will choose all white elements whose indices are multiples of the index of at least one black element and colour those elements green. After that, her score is the maximum value of a_i out of all black and green elements.There are 2^n-1 ways for Chaneka to choose the black indices. Find the sum of scores for all possible ways Chaneka can choose the black indices. Since the answer can be very big, print the answer modulo 998\,244\,353.InputThe first line contains a single integer n (1 \leq n \leq 10^5) — the size of array a.The second line contains n integers a_1,a_2,a_3,\ldots,a_n (0\leq a_i\leq10^5).OutputAn integer representing the sum of scores for all possible ways Chaneka can choose the black indices, modulo 998\,244\,353.ExamplesInput
4
19 14 19 9
Output
265
Input
1
0
Output
0
Input
15
90000 9000 99000 900 90900 9900 99900 90 90090 9090 99090 990 90990 9990 99990
Output
266012571
NoteIn the first example, below are the 15 possible ways to choose the black indices:   Index 1 is black. Indices 2, 3, and 4 are green. Maximum value among them is 19.  Index 2 is black. Index 4 is green. Maximum value among them is 14.  Index 3 is black. Maximum value among them is 19.  Index 4 is black. Maximum value among them is 9.  Indices 1 and 2 are black. Indices 3 and 4 are green. Maximum value among them is 19.  Indices 1 and 3 are black. Indices 2 and 4 are green. Maximum value among them is 19.  Indices 1 and 4 are black. Indices 2 and 3 are green. Maximum value among them is 19.  Indices 2 and 3 are black. Index 4 is green. Maximum value among them is 19.  Indices 2 and 4 are black. Maximum value among them is 14.  Indices 3 and 4 are black. Maximum value among them is 19.  Indices 1, 2, and 3 are black. Index 4 is green. Maximum value among them is 19.  Indices 1, 2, and 4 are black. Index 3 is green. Maximum value among them is 19.  Indices 1, 3, and 4 are black. Index 2 is green. Maximum value among them is 19.  Indices 2, 3, and 4 are black. Maximum value among them is 19.  Indices 1, 2, 3, and 4 are black. Maximum value among them is 19. The total sum is 19+14+19+9+19+19+19+19+14+19+19+19+19+19+19 = 265.
4
19 14 19 9

265 
['combinatorics', 'number theory', 'sortings', '*1500']