#!/usr/bin/env python3
if __name__ == '__main__':
    target = 277678
    xstep = 1
    ystep = 1
    origin = [0, 0]
    square = 1
    pointer = origin

    def inc_step(step):
      if step >= 0:
        return int(-1 * (step + 1))
      else:
        return int(-1 * (step - 1))

    while square < target:
      i = 1
      while i <= abs(xstep) and square < target:
        square += 1
        if xstep >= 0:
          pointer[0] += 1
        else:
          pointer[0] += -1
        i += 1
      xstep = inc_step(xstep)

      i = 1
      while i <= abs(ystep) and square < target:
        square += 1
        if ystep >= 0:
          pointer[1] += 1
        else:
          pointer[1] += -1
        i += 1
      ystep = inc_step(ystep)

    if square == target:
      xloc = pointer[0]
      yloc = pointer[1]
      distance = abs(xloc) + abs(yloc)
      print(f"dist to square {target} is {int(abs(xloc))}+{int(abs(yloc))}={distance}")