Score : $700$ points

Problem Statement

Given is a sequence of $N$ integers $A_1,A_2,\ldots,A_N$. Print the number, modulo $998244353$, of sequences of $N$ integers $X_1,X_2,\ldots,X_N$ satisfying all of the following conditions:

• $1 \leq X_i \leq A_i$
• $X_i \neq X_{i+1} (1 \leq i \leq N-1)$

Constraints

• $2 \leq N \leq 5 \times 10^5$
• $1 \leq A_i \leq 10^9$

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print the answer.

3
2 3 2

6

The following six sequences satisfy all of the conditions.

• $1,2,1$
• $1,3,1$
• $1,3,2$
• $2,1,2$
• $2,3,1$
• $2,3,2$

10
158260522 877914575 602436426 24979445 861648772 623690081 433933447 476190629 262703497 211047202

524691026