F. Non-equal Neighbours
combinatorics; dp; math
You are given an array of \(n\) positive integers \(a_1, a_2, \ldots, a_n\). Your task is to calculate the number of arrays of \(n\) positive integers \(b_1, b_2, \ldots, b_n\) such that: \(1 \le b_i \le a_i\) for every \(i\) (\(1 \le i \le n\)), and \(b_i \neq b_{i+1}\) for every \(i\) (\(1 \le i \le n - 1\)). The number of such arrays can be very large, so print it modulo \(998\,244\,353\).
The first line contains a single integer \(n\) (\(1 \le n \le 2 \cdot 10^5\)) — the length of the array \(a\).The second line contains \(n\) integers \(a_1, a_2, \ldots, a_n\) (\(1 \le a_i \le 10^9\)).
Print the answer modulo \(998\,244\,353\) in a single line.
In the first test case possible arrays are \([1, 2, 1]\) and \([2, 1, 2]\).In the second test case possible arrays are \([1, 2]\), \([1, 3]\), \([2, 1]\) and \([2, 3]\).