201533: [AtCoder]ARC153 D - Sum of Sum of Digits

Problem Statement

For a positive integer $x$, let $f(x)$ denote the sum of its digits. For instance, we have $f(153) = 1 + 5 + 3 = 9$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$.

You are given a sequence of positive integers $A = (A_1, \ldots, A_N)$. Find the minimum possible value of $\sum_{i=1}^N f(A_i + x)$ where $x$ is a non-negative integer.

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq A_i < 10^9$

Input

The input is given from Standard Input in the following format:

$N$
$A_1$ $\ldots$ $A_N$

Output

Print the minimum possible value of $\sum_{i=1}^N f(A_i + x)$ where $x$ is a non-negative integer.

Sample Input 1

4
4 13 8 6

Sample Output 1

14

For instance, $x = 7$ makes $\sum_{i=1}^N f(A_i+x) = f(11) + f(20) + f(15) + f(13) = 14$.

Sample Input 2

4
123 45 678 90

Sample Output 2

34

For instance, $x = 22$ makes $\sum_{i=1}^N f(A_i+x) = f(145) + f(67) + f(700) + f(112) = 34$.

Sample Input 3

3
1 10 100

Sample Output 3

3

For instance, $x = 0$ makes $\sum_{i=1}^N f(A_i+x) = f(1) + f(10) + f(100) = 3$.

Sample Input 4

1
153153153

Sample Output 4

1

For instance, $x = 9999846846847$ makes $\sum_{i=1}^N f(A_i+x) = f(10000000000000) = 1$.