For 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.