#  File: Triangle.py

#  Description:

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#  Course Name: CS 313E

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import sys

from timeit import timeit

# returns the greatest path sum using exhaustive search
def brute_force (grid):
  return

# returns the greatest path sum using greedy approach
def greedy (grid):
  return

# returns the greatest path sum using divide and conquer (recursive) approach
def divide_conquer (grid):
  return

# returns the greatest path sum and the new grid using dynamic programming
def dynamic_prog (grid):
  return

# reads the file and returns a 2-D list that represents the triangle
def read_file ():
  # read number of lines
  line = sys.stdin.readline()
  line = line.strip()
  n = int (line)

  # create an empty grid with 0's
  grid = [[0 for i in range (n)] for j in range (n)]

  # read each line in the input file and add to the grid
  for i in range (n):
    line = sys.stdin.readline()
    line = line.strip()
    row = line.split()
    row = list (map (int, row))
    for j in range (len(row)):
      grid[i][j] = grid[i][j] + row[j]

  return grid 

def main ():
  # read triangular grid from file
  grid = read_file()
  
  '''
  # check that the grid was read in properly
  print (grid)
  '''

  # output greatest path from exhaustive search
  times = timeit ('brute_force({})'.format(grid), 'from __main__ import brute_force', number = 10)
  times = times / 10
  # print time taken using exhaustive search

  # output greatest path from greedy approach
  times = timeit ('greedy({})'.format(grid), 'from __main__ import greedy', number = 10)
  times = times / 10
  # print time taken using greedy approach

  # output greatest path from divide-and-conquer approach
  times = timeit ('divide_conquer({})'.format(grid), 'from __main__ import divide_conquer', number = 10)
  times = times / 10
  # print time taken using divide-and-conquer approach

  # output greatest path from dynamic programming 
  times = timeit ('dynamic_prog({})'.format(grid), 'from __main__ import dynamic_prog', number = 10)
  times = times / 10
  # print time taken using dynamic programming

if __name__ == "__main__":
  main()