Non-equal Neighbours

3000ms

524288K

Description:

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 $$$998\,244\,353$$$.

Input:

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 $$$a_1, a_2, \ldots, a_n$$$ ($$$1 \le a_i \le 10^9$$$).

Output:

Print the answer modulo $$$998\,244\,353$$$ in a single line.

Sample Input:

3
2 2 2

Sample Output:

Sample Input:

2
2 3

Sample Output:

Sample Input:

3
1 1 1

Sample Output:

Note:

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 $$$[2, 3]$$$.

Informação

Provedor Codeforces

Código CF1585F