1971F - Circle Perimeter - CodeForces Solution

import math

def count(r):
    count = 1+4*r+4*(sum(math.isqrt(r**2-a**2) for a in range(1,r)))
    return count
def c_cir(r):
	result = 0
	for x in range(1, r):
	    ySquare = r*r - x*x 
	    y = int(math.sqrt(ySquare))
	    if (y*y == ySquare):result += 4
	return result 
for _ in range(int(input())):
    r = int(input())
    print(count(r+1)-count(r)-c_cir(r+1)+c_cir(r))