Problem Statement

There are N squares called Square 1 though Square N. You start on Square 1.
Each of the squares from Square 1 through Square N-1 has a die on it. The die on Square i is labeled with the integers from 0 through A_i, each occurring with equal probability. (Die rolls are independent of each other.)
Until you reach Square N, you will repeat rolling a die on the square you are on. Here, if the die on Square x rolls the integer y, you go to Square x+y.
Find the expected value, modulo 998244353, of the number of times you roll a die.

Input

Input is given from Standard Input in the following format:
N
$A_1 A_2 \dots A_{N-1}$

Output

Print the answer.

Constraints

• $2 \le N \le 2 \times 10^5$
• $1 \le A_i \le N-i(1 \le i \le N-1)$
• All values in input are integers.

Sample Input 1

3
1 1

Sample Output 1

4

The sought expected value is 4, so 4 should be printed.
Here is one possible scenario until reaching Square N:

• Roll 1 on Square 1, and go to Square 2.
• Roll 0 on Square 2, and stay there.
• Roll 1 on Square 2, and go to Square 3.

This scenario occurs with probability $\frac{1}{8}$.

Sample Input 2

5
3 1 2 1

Sample Output 2

332748122

见题面 Input 部分

见题面 Output 部分