#!/usr/bin/env python3

from math import gcd

def sols():
    """yields solutions to a**2 - 2b**2 = -1"""
    a, b = 3, 2
    while True:
        yield 2*b - a, a - b
        a, b = 3*a + 4*b, 2*a + 3*b


def mn_from_ab(a, b, sgn):
    M, N = a + b, b - sgn
    div = gcd(M, N)
    m, n = M // div, N // div
    return m, n

def gen_mn(N):
    for a, b in sols():
        if b > N//2:
            break
        yield mn_from_ab(a, b, 1)
        yield mn_from_ab(a, b, -1)

def is_primitive(m, n):
    return (m + n) % 2 == 1 and n != 0

def count_triangles(m, n, circ):
    sides = (m**2 - n**2, 2*m*n, m**2 + n**2)
    return (circ-1) // sum(sides)

N = 100 * 10**6

R = sum(count_triangles(m, n, N) for m, n in gen_mn(N) if is_primitive(m, n))
print(R)