Codeforces celebrates 10 years! We are pleased to announce the crowdfunding-campaign. Congratulate us by the link https://codeforces.com/10years. ×

D. Yet Another Problem On a Subsequence
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

The sequence of integers $$$a_1, a_2, \dots, a_k$$$ is called a good array if $$$a_1 = k - 1$$$ and $$$a_1 > 0$$$. For example, the sequences $$$[3, -1, 44, 0], [1, -99]$$$ are good arrays, and the sequences $$$[3, 7, 8], [2, 5, 4, 1], [0]$$$ — are not.

A sequence of integers is called good if it can be divided into a positive number of good arrays. Each good array should be a subsegment of sequence and each element of the sequence should belong to exactly one array. For example, the sequences $$$[2, -3, 0, 1, 4]$$$, $$$[1, 2, 3, -3, -9, 4]$$$ are good, and the sequences $$$[2, -3, 0, 1]$$$, $$$[1, 2, 3, -3 -9, 4, 1]$$$ — are not.

For a given sequence of numbers, count the number of its subsequences that are good sequences, and print the number of such subsequences modulo 998244353.

Input

The first line contains the number $$$n~(1 \le n \le 10^3)$$$ — the length of the initial sequence. The following line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n~(-10^9 \le a_i \le 10^9)$$$ — the sequence itself.

Output

In the single line output one integer — the number of subsequences of the original sequence that are good sequences, taken modulo 998244353.

Examples
Input
3
2 1 1
Output
2
Input
4
1 1 1 1
Output
7
Note

In the first test case, two good subsequences — $$$[a_1, a_2, a_3]$$$ and $$$[a_2, a_3]$$$.

In the second test case, seven good subsequences — $$$[a_1, a_2, a_3, a_4], [a_1, a_2], [a_1, a_3], [a_1, a_4], [a_2, a_3], [a_2, a_4]$$$ and $$$[a_3, a_4]$$$.