Problem:
Score : 200 points

Problem Statement

AtCoDeer the deer found two rectangles lying on the table, each with height 1 and width W.
If we consider the surface of the desk as a two-dimensional plane, the first rectangle covers the vertical range of [0,1] and the horizontal range of [a,a+W], and the second rectangle covers the vertical range of [1,2] and the horizontal range of [b,b+W], as shown in the following figure:

AtCoDeer will move the second rectangle horizontally so that it connects with the first rectangle.
Find the minimum distance it needs to be moved.

Constraints

All input values are integers.

1≤W≤10^5

1≤a,b≤10^5

Input

The input is given from Standard Input in the following format:

W a b

Output

Print the minimum distance the second rectangle needs to be moved.

Sample Input 1

3 2 6

Sample Output 1

1

This input corresponds to the figure in the statement. In this case, the second rectangle should be moved to the left by a distance of 1.

Sample Input 2

3 1 3

Sample Output 2

0

The rectangles are already connected, and thus no move is needed.

Sample Input 3

5 10 1

Sample Output 3

4

Solution in Python (3.4.3) (judge verdict: Runtime Error)

import numpy as np

def main():

  N = int(input())
  A = list(map(int, input().split()))

  su = np.sum(A)
  av = su // N
  if su % N != 0:
    print(-1)
    return

  ans = N - 1
  b = 0
  c = 0

  for a in A[0: -1]:
    b += a
    c += 1
    if b == (c * av):
      ans -= 1
      b = 0
      c = 0

  print(ans)

main()