F. Circle Perimeter
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given an integer $$$r$$$, find the number of lattice points that have a Euclidean distance from $$$(0, 0)$$$ greater than or equal to $$$r$$$ but strictly less than $$$r+1$$$.

A lattice point is a point with integer coordinates. The Euclidean distance from $$$(0, 0)$$$ to the point $$$(x,y)$$$ is $$$\sqrt{x^2 + y^2}$$$.

Input

The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 1000$$$) — the number of test cases.

The only line of each test case contains a single integer $$$r$$$ ($$$1 \leq r \leq 10^5$$$).

The sum of $$$r$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, output a single integer — the number of lattice points that have an Euclidean distance $$$d$$$ from $$$(0, 0)$$$ such that $$$r \leq d < r+1$$$.

Example
Input
6
1
2
3
4
5
1984
Output
8
16
20
24
40
12504
Note

The points for the first three test cases are shown below.