F. Count Pairs
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

You will be asked $$$Q$$$ queries. In each query, you will be given an integer number $$$k$$$ and you have to find out the number of ordered integer pairs($$$x,y$$$) satisfying the equation, $$$x^2+y^2 \le k$$$.

Input

$$$1 \le Q \le 10^5$$$

$$$-10^3\le k\le 10^3$$$

Output

For each query, print an integer the number of ordered interger pairs($$$x,y$$$) satisfying the equation, $$$x^2+y^2 \le k$$$.

Example
Input
3
2
0
5
Output
9
1
21