Nested Summation over Subarrays

Given a sequence a of length n, consider every contiguous subarray (interval) [l, r] of a. For a subarray of length m = r-l+1, define its value as follows:

If there exists any index k (with 1 ≤ k ≤ m) such that k > a[l+k-1], then the value of the subarray is 0. Otherwise, the value is given by the nested summation

$$S_{l,r} = \sum_{i_1=1}^{a_l}\sum_{i_2=2}^{a_{l+1}}\cdots\sum_{i_m=m}^{a_r} \Bigl(i_1+i_2+\cdots+i_m\Bigr). $$

The answer to the problem is the sum of S_l,r over all subarrays [l, r] modulo 998244353.

inputFormat

The first line contains an integer n — the length of the sequence.

The second line contains n space-separated integers representing the sequence a.

outputFormat

Print a single integer — the sum of the values of all subarrays computed as described above, taken modulo 998244353.

sample

1
1

1

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