codeforces#P1971F. Circle Perimeter
Circle Perimeter
Description
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 $\sqrt{x^2 + y^2}$.
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 $10^5$.
For each test case, output a single integer — the number of lattice points that have an Euclidean distance $d$ from $(0, 0)$ such that $r \leq d < r+1$.
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 $r \leq d < r+1$.
6
1
2
3
4
5
1984
8
16
20
24
40
12504
Note
The points for the first three test cases are shown below.
