Another Sigma Problem

AtCoder

IDabc353_d

Time2000ms

Memory256MB

Difficulty—

For positive integers $x$ and $y$, define $f(x, y)$ as follows: * Interpret the decimal representations of $x$ and $y$ as strings and concatenate them in this order to obtain a string $z$. The value of $f(x, y)$ is the value of $z$ when interpreted as a decimal integer. For example, $f(3, 14) = 314$ and $f(100, 1) = 1001$. You are given a sequence of positive integers $A = (A_1, \ldots, A_N)$ of length $N$. Find the value of the following expression modulo $998244353$: $\displaystyle \sum_{i=1}^{N-1}\sum_{j=i+1}^N f(A_i,A_j)$. ## Constraints * $2 \leq N \leq 2 \times 10^5$ * $1 \leq A_i \leq 10^9$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $\ldots$ $A_N$ [samples]

Samples

Input #1

3
3 14 15

Output #1

2044

*   $f(A_1, A_2) = 314$
*   $f(A_1, A_3) = 315$
*   $f(A_2, A_3) = 1415$

Thus, the answer is $f(A_1, A_2) + f(A_1, A_3) + f(A_2, A_3) = 2044$.

Input #2

5
1001 5 1000000 1000000000 100000

Output #2

625549048

Be sure to calculate the value modulo $998244353$.

API Response (JSON)

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