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.

Sample Input 1

3
2 3 2

Sample Output 1

6

The following six sequences satisfy all of the conditions.

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

Sample Input 2

10
158260522 877914575 602436426 24979445 861648772 623690081 433933447 476190629 262703497 211047202

Sample Output 2

524691026