C. Extreme Extensiontime limit per test4 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputFor an array b of n integers, the extreme value of this array is the minimum number of times (possibly, zero) the following operation has to be performed to make b non-decreasing:   Select an index i such that 1 \le i \le |b|, where |b| is the current length of b.  Replace b_i with two elements x and y such that x and y both are positive integers and x + y = b_i.  This way, the array b changes and the next operation is performed on this modified array. For example, if b = [2, 4, 3] and index 2 gets selected, then the possible arrays after this operation are [2, \underline{1}, \underline{3}, 3], [2, \underline{2}, \underline{2}, 3], or [2, \underline{3}, \underline{1}, 3]. And consequently, for this array, this single operation is enough to make it non-decreasing: [2, 4, 3] \rightarrow [2, \underline{2}, \underline{2}, 3].It's easy to see that every array of positive integers can be made non-decreasing this way.YouKn0wWho has an array a of n integers. Help him find the sum of extreme values of all nonempty subarrays of a modulo 998\,244\,353. If a subarray appears in a multiple times, its extreme value should be counted the number of times it appears.An array d is a subarray of an array c if d can be obtained from c by deletion of several (possibly, zero or all) elements from the beginning and several (possibly, zero or all) elements from the end.InputThe first line contains a single integer t (1 \le t \le 10\,000) — the number of test cases.The first line of each test case contains a single integer n (1 \le n \le 10^5).The second line of each test case contains n integers a_1, a_2, \ldots, a_n (1 \le a_i \le 10^5).It is guaranteed that the sum of n over all test cases doesn't exceed 10^5.OutputFor each test case, print a single integer  — the sum of extreme values of all subarrays of a modulo 998\,244\,353.ExampleInput
4
3
5 4 3
4
3 2 1 4
1
69
8
7264 40515 28226 92776 35285 21709 75124 48163
Output
5
9
0
117
NoteLet f(l, r) denote the extreme value of [a_l, a_{l+1}, \ldots, a_r].In the first test case,   f(1, 3) = 3, because YouKn0wWho can perform the following operations on the subarray [5, 4, 3] (the newly inserted elements are underlined):[5, 4, 3] \rightarrow [\underline{3}, \underline{2}, 4, 3] \rightarrow [3, 2, \underline{2}, \underline{2}, 3] \rightarrow [\underline{1}, \underline{2}, 2, 2, 2, 3]; f(1, 2) = 1, because [5, 4] \rightarrow [\underline{2}, \underline{3}, 4]; f(2, 3) = 1, because [4, 3] \rightarrow [\underline{1}, \underline{3}, 3]; f(1, 1) = f(2, 2) = f(3, 3) = 0, because they are already non-decreasing. So the total sum of extreme values of all subarrays of a = 3 + 1 + 1 + 0 + 0 + 0 = 5.
4
3
5 4 3
4
3 2 1 4
1
69
8
7264 40515 28226 92776 35285 21709 75124 48163

5 9 0 117 
['dp', 'greedy', 'math', 'number theory', '*2300']