Problem Statement

There is a row of $N squares labeled 1,2,\dots,N$ and $a sequence A=(A_1,A_2,\dots,A_N)$ of length N.
Initially, square 1 is painted black, the other N-1 squares are painted white, and a piece is placed on square 1.
You may repeat the following operation any number of times, possibly zero:

• When the piece is on square i, choose a positive integer x and move the piece to square $i + A_i \times x$.

• Here, you cannot make a move with $i + A_i \times x > N$.

• Then, paint the square $i + A_i \times x$ black.

Find the number of possible sets of squares that can be painted black at the end of the operations, modulo 998244353.

Input

The input is given from Standard Input in the following format:
N
$A_1 A_2 \dots A_N$

Output

Print the answer as an integer.

Constraints

• All input values are integers.
• $1 \le N \le 2 \times 10^5$
• $1 \le A_i \le 2 \times 10^5$

Sample Input 1

5
1 2 3 1 1

Sample Output 1

8

There are eight possible sets of squares painted black:

• Square 1
• Squares 1,2
• Squares 1,2,4
• Squares 1,2,4,5
• Squares 1,3
• Squares 1,4
• Squares 1,4,5
• Squares 1,5

Sample Input 2

1
200000

Sample Output 2

1

Sample Input 3

40
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Sample Output 3

721419738

Be sure to find the number modulo 998244353.

见题面 Input 部分

见题面 Output 部分