'''Function L(r) counts number of lattice points inside a circle of radius r, where a lattice point is a point (m, n) with integer coordinates. L(r) converges to the area of a circle with radius r.'''

def L(r):
    count = 0
    pairs = [0, 0]
    for i in range(-r, r + 1):
        pairs[0] = i
        for j in range(-r, r + 1):
            pairs[1] = j
            if ((pairs[0] ** 2) + (pairs[1] ** 2)) ** 0.5 <= r:
                count += 1
    return count