import numpy as np
from numpy import dot
import math
from math import pi


#returns smallest power of 2 that is greater or equal than v
def power_2_bound(v):
    v -= 1
    v |= v >> 1
    v |= v >> 2
    v |= v >> 4
    v |= v >> 8
    v |= v >> 16
    return v + 1

#complex mul and add
def cdot(x, y):
    return np.array([x[0] * y[0] - x[1] * y[1], x[0] * y[1] + x[1] * y[0]])

def cadd(x, y):
    return np.array([x[0] + y[0], x[1] + y[1]])

np.set_printoptions(suppress=True)
resolution = power_2_bound(n)
root_angles = np.array([(2 * math.pi) * i / resolution for i in xrange(resolution)])
roots = np.array([np.cos(root_angles), np.sin(root_angles)])

for i in xrange(resolution):
    for j in xrange(resolution):
        print i, j, cdot(roots[:, i], roots[:, j]), roots[:, (i + j)%resolution]