prompt: You will be provided with a partial code base and an issue statement explaining a problem to resolve.
  <issue>
  ProjectEuler -- Problem 1 -- solv2.py -- Error
  For the Input ```1000``` I get ```233366.4```. The correct answer should be ```233168``` 
  See [file](https://github.com/TheAlgorithms/Python/blob/master/Project%20Euler/Problem%2001/sol2.py)
  
  </issue>
  <code>
  [start of Project Euler/Problem 01/sol2.py]
  1 '''
  2 Problem Statement:
  3 If we list all the natural numbers below 10 that are multiples of 3 or 5,
  4 we get 3,5,6 and 9. The sum of these multiples is 23.
  5 Find the sum of all the multiples of 3 or 5 below N.
  6 '''
  7 from __future__ import print_function
  8 try:
  9     raw_input          # Python 2
  10 except NameError:
  11     raw_input = input  # Python 3
  12 n = int(raw_input().strip())
  13 sum = 0
  14 terms = (n-1)/3
  15 sum+= ((terms)*(6+(terms-1)*3))/2 #sum of an A.P.
  16 terms = (n-1)/5
  17 sum+= ((terms)*(10+(terms-1)*5))/2
  18 terms = (n-1)/15
  19 sum-= ((terms)*(30+(terms-1)*15))/2
  20 print(sum)
  21
  [end of Project Euler/Problem 01/sol2.py]
  </code>
  
  I need you to solve this issue by generating a single patch file that I can apply directly to this repository using git apply. Please respond with a single patch file in the following format.
  <patch>
  diff --git a/file.py b/file.py
  --- a/file.py
  +++ b/file.py
  @@ -1,27 +1,35 @@
   def euclidean(a, b):
  -    while b:
  -        a, b = b, a % b
  -    return a
  +    if b == 0:
  +        return a
  +    return euclidean(b, a % b)
   
   
   def bresenham(x0, y0, x1, y1):
       points = []
       dx = abs(x1 - x0)
       dy = abs(y1 - y0)
  -    sx = 1 if x0 < x1 else -1
  -    sy = 1 if y0 < y1 else -1
  -    err = dx - dy
  +    x, y = x0, y0
  +    sx = -1 if x0 > x1 else 1
  +    sy = -1 if y0 > y1 else 1
   
  -    while True:
  -        points.append((x0, y0))
  -        if x0 == x1 and y0 == y1:
  -            break
  -        e2 = 2 * err
  -        if e2 > -dy:
  -            err -= dy
  -            x0 += sx
  -        if e2 < dx:
  -            err += dx
  -            y0 += sy
  +    if dx > dy:
  +        err = dx / 2.0
  +        while x != x1:
  +            points.append((x, y))
  +            err -= dy
  +            if err < 0:
  +                y += sy
  +                err += dx
  +            x += sx
  +    else:
  +        err = dy / 2.0
  +        while y != y1:
  +            points.append((x, y))
  +            err -= dx
  +            if err < 0:
  +                x += sx
  +                err += dy
  +            y += sy
  +
  +    points.append((x, y))
       return points
  
  </patch>
golden_diff: diff --git a/Project Euler/Problem 01/sol2.py b/Project Euler/Problem 01/sol2.py
  --- a/Project Euler/Problem 01/sol2.py	
  +++ b/Project Euler/Problem 01/sol2.py	
  @@ -11,10 +11,10 @@
       raw_input = input  # Python 3
   n = int(raw_input().strip())
   sum = 0
  -terms = (n-1)/3
  -sum+= ((terms)*(6+(terms-1)*3))/2 #sum of an A.P.
  -terms = (n-1)/5
  -sum+= ((terms)*(10+(terms-1)*5))/2
  -terms = (n-1)/15
  -sum-= ((terms)*(30+(terms-1)*15))/2
  +terms = (n-1)//3
  +sum+= ((terms)*(6+(terms-1)*3))//2 #sum of an A.P.
  +terms = (n-1)//5
  +sum+= ((terms)*(10+(terms-1)*5))//2
  +terms = (n-1)//15
  +sum-= ((terms)*(30+(terms-1)*15))//2
   print(sum)
  
verification_info: {"golden_diff": "diff --git a/Project Euler/Problem 01/sol2.py b/Project Euler/Problem 01/sol2.py\n--- a/Project Euler/Problem 01/sol2.py\t\n+++ b/Project Euler/Problem 01/sol2.py\t\n@@ -11,10 +11,10 @@\n     raw_input = input  # Python 3\n n = int(raw_input().strip())\n sum = 0\n-terms = (n-1)/3\n-sum+= ((terms)*(6+(terms-1)*3))/2 #sum of an A.P.\n-terms = (n-1)/5\n-sum+= ((terms)*(10+(terms-1)*5))/2\n-terms = (n-1)/15\n-sum-= ((terms)*(30+(terms-1)*15))/2\n+terms = (n-1)//3\n+sum+= ((terms)*(6+(terms-1)*3))//2 #sum of an A.P.\n+terms = (n-1)//5\n+sum+= ((terms)*(10+(terms-1)*5))//2\n+terms = (n-1)//15\n+sum-= ((terms)*(30+(terms-1)*15))//2\n print(sum)\n", "issue": "ProjectEuler -- Problem 1 -- solv2.py -- Error\nFor the Input ```1000``` I get ```233366.4```. The correct answer should be ```233168``` \r\nSee [file](https://github.com/TheAlgorithms/Python/blob/master/Project%20Euler/Problem%2001/sol2.py)\n", "before_files": [{"content": "'''\nProblem Statement:\nIf we list all the natural numbers below 10 that are multiples of 3 or 5,\nwe get 3,5,6 and 9. The sum of these multiples is 23.\nFind the sum of all the multiples of 3 or 5 below N.\n'''\nfrom __future__ import print_function\ntry:\n    raw_input          # Python 2\nexcept NameError:\n    raw_input = input  # Python 3\nn = int(raw_input().strip())\nsum = 0\nterms = (n-1)/3\nsum+= ((terms)*(6+(terms-1)*3))/2 #sum of an A.P.\nterms = (n-1)/5\nsum+= ((terms)*(10+(terms-1)*5))/2\nterms = (n-1)/15\nsum-= ((terms)*(30+(terms-1)*15))/2\nprint(sum)\n", "path": "Project Euler/Problem 01/sol2.py"}]}