Problem Statement

For a positive integer $x$, let $f(x)$ denote the sum of its digits. For instance, $f(158) = 1 + 5 + 8 = 14$, $f(2023) = 2 + 0 + 2 + 3 = 7$, and $f(1) = 1$.

You are given a sequence of positive integers $A = (A_1, \\ldots, A_N)$. Find $\\sum_{i=1}^N\\sum_{j=1}^N f(A_i + A_j)$.

Constraints

• $1\\leq N\\leq 2\\times 10^5$
• $1\\leq A_i < 10^{15}$

Input

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

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

Output

Print $\\sum_{i=1}^N\\sum_{j=1}^N f(A_i + A_j)$.

Sample Input 1

2
53 28

Sample Output 1

36

We have $\\sum_{i=1}^N\\sum_{j=1}^N f(A_i + A_j) = f(A_1+A_1)+f(A_1+A_2)+f(A_2+A_1)+f(A_2+A_2)=7+9+9+11=36$.

Sample Input 2

1
999999999999999

Sample Output 2

135

We have $\\sum_{i=1}^N\\sum_{j=1}^N f(A_i + A_j) = f(A_1+A_1) = 135$.

Sample Input 3

5
123 456 789 101 112

Sample Output 3

321