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 $r \leq d < r+1$.

见题面 Input 部分

见题面 Output 部分

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