Problem Statement

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:
$\displaystyle \sum_{i=1}^{N-1}\sum_{j=i+1}^N f(A_i,A_j)$.

Input

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

Output

Print the answer.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^9$
• All input values are integers.

Sample Input 1

3
3 14 15

Sample 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.

Sample Input 2

5
1001 5 1000000 1000000000 100000

Sample Output 2

625549048

Be sure to calculate the value modulo 998244353.

见题面 Input 部分

见题面 Output 部分