#!/usr/bin/python
"""Extract an orthonormal basis from a matrix, inefficiently.

This is maybe not as interesting as I thought it was initially, since
it's not clear what relationship the new orthonormal basis has to the
original matrix, except that it spans the same subspace orthonormally;
and it leaves any orthonormal prefix of the original matrix
undisturbed.

It's inefficient because it does O(N**3) work for an NxN matrix, and
also because it's doing all the work in (presumably interpreted)
Python.

"""

import sys
import math

class Vector:
    def __init__(self, contents):
        self.contents = contents

    def project_onto(self, other):
        # XXX why does this stop working when I replace
        # other.magnitude()**2 with other.dot(other)?
        return other.scaled_by(self.dot(other) / other.magnitude()**2)

    def magnitude(self):
        return math.sqrt(self.dot(self))

    def scaled_by(self, c):
        return Vector([x * c for x in self.contents])

    def dot(self, other):
        return sum(a*b for a, b in zip(self.contents, other.contents))

    def __add__(self, other):
        return Vector([a+b for a, b in zip(self.contents, other.contents)])

    def __sub__(self, other):
        return Vector([a-b for a, b in zip(self.contents, other.contents)])

    def __str__(self):
        return ' '.join(str(x) for x in self.contents)

def orthonormal_basis(input_rows):
    rows = []
    for nums in input_rows:
        for row in rows:
            nums -= nums.project_onto(row)
        nums = nums.scaled_by(1/nums.magnitude())
        rows.append(nums)
        yield nums
        
def main():
    rows = list(orthonormal_basis(Vector([int(field) for field in line.split()])
                                  for line in sys.stdin))
    for row in rows: print row

    print "dot products:"

    for a in rows:
        for b in rows:
            print a.dot(b),
        print

if __name__ == '__main__':
    main()