class BinHeap:
   
   def __init__(self, a_list=[]):
      """Constructs a BinHeap object.
      
      Can either create an empty BinHeap or can construct it from a_list.
      """
      self.heap_list = [0] + a_list
      for i in range(self.size() // 2, 0, -1):
         self.perc_down(i)
         
   def size(self):
      """Return the size of the heap."""
      return len(self.heap_list) - 1   

   def perc_up(self, i):
      """Percolate element i up the heap to its correct position."""
      while i // 2 > 0 and self.heap_list[i] < self.heap_list[i // 2]:
         self.heap_list[i], self.heap_list[i // 2] = \
            self.heap_list[i // 2], self.heap_list[i]
         i = i // 2
      
   def insert(self, k):
      """Insert k into the heap."""
      self.heap_list.append(k)
      self.perc_up(self.size())
   
   def perc_down(self, i):
      """Percolate element i down the heap to its correct position."""
      while (i * 2) <= self.size():
         child = self.min_child(i)
         if self.heap_list[i] > self.heap_list[child]:
            self.heap_list[child], self.heap_list[i] = \
               self.heap_list[i], self.heap_list[child]
         i = child
   
   def min_child(self, i):
      """Return the index of the minimum child of index i."""
      left = i * 2
      right = left + 1
      if right > self.size():
         return left
      return left if self.heap_list[left] < self.heap_list[right] else right
         
   def del_min(self):
      """Extract and return the minimum value from the heap."""
      ret_val = self.heap_list[1]
      replacement = self.heap_list.pop()
      if self.size() > 0:
         self.heap_list[1] = replacement
      self.perc_down(1)
      return ret_val
         
   def __str__(self):
      """Return the readable string of the heap."""
      return str(self.heap_list[1:])
         
# We make the heap in two different ways
# and compare the output.
bh = BinHeap()
print(bh)
bh.insert(9)
bh.insert(6)
bh.insert(5)
bh.insert(2)
bh.insert(3)
print(bh)

while bh.size() > 0:
   print(bh.del_min())
   print(bh)

bh = BinHeap([9,6,5,2,3])
print(bh)

while bh.size() > 0:
   print(bh.del_min())
   print(bh)