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H. Sum of Digits of Sums
time limit per test
6 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given an array $$$[a_1, a_2, \dots, a_n]$$$, consisting of positive integers.

For every $$$i$$$ from $$$1$$$ to $$$n$$$, calculate $$$\sum \limits_{j=1}^{n} F(a_i + a_j)$$$, where $$$F(x)$$$ is the sum of digits of $$$x$$$.

Input

The first line contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$).

The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i < 10^9$$$).

Output

Print $$$n$$$ integers. The $$$i$$$-th of them should be equal to $$$\sum \limits_{j=1}^{n} F(a_i + a_j)$$$.

Examples
Input
4
1 3 3 7
Output
18 17 17 15
Input
3
42 1337 999
Output
38 53 47