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You and Me (NAVILLERA)

Time limit1sMemory limit1024 MB

Summary
Find the minimum number of moves, each of exact length c in the plane, needed to go from (0,0) to (X,Y).
Level

Medium4 of 10

Topics
Math, Geometry
Solved
No attempts yet

Problem

Flying like a butterfly, nana na na, I dance along

Wind, wind, blow

Flutter so I can fly over to you

With a pure white heart

I want to fly toward you like a butterfly. I am at the point (0,0)(0,0) on the coordinate plane, and you are at (X,Y)(X,Y).

To fly like a butterfly, I can flap my wings zero or more times.

If I flap once from position (a,b)(a,b), I can move to any (x,y)(x,y) that satisfies (x−a)2+(y−b)2=c2(x-a)^2+(y-b)^2=c^2.

Find the minimum number of flaps needed to reach your position (X,Y)(X,Y).

Input

The first line contains XX, YY, and cc.

Output

On the first line, print the minimum number of flaps.

Constraints

  • −104≤X,Y≤104-10^4\leq X,Y\leq 10^4
  • 1≤c≤1041\leq c\leq 10^{4}
  • All numbers in the input are integers.

Examples5

  1. Example 1

    Input
    4 3 4
    Expected output
    2

  2. Example 2

    Input
    1 1 10
    Expected output
    2

  3. Example 3

    Input
    3 4 5
    Expected output
    1

  4. Example 4

    Input
    10 0 1
    Expected output
    10

  5. Example 5

    Input
    0 0 1
    Expected output
    0