Problem:
Score: 300 points

Problem Statement

In the Ancient Kingdom of Snuke, there was a pyramid to strengthen the authority of Takahashi, the president of AtCoder Inc.

The pyramid had center coordinates (C_X, C_Y) and height H. The altitude of coordinates (X, Y) is max(H - |X - C_X| - |Y - C_Y|, 0).

Aoki, an explorer, conducted a survey to identify the center coordinates and height of this pyramid. As a result, he obtained the following information:

C_X, C_Y was integers between 0 and 100 (inclusive), and H was an integer not less than 1.

Additionally, he obtained N pieces of information. The i-th of them is: "the altitude of point (x_i, y_i) is h_i."

This was enough to identify the center coordinates and the height of the pyramid. Find these values with the clues above.

Constraints

N is an integer between 1 and 100 (inclusive).

x_i and y_i are integers between 0 and 100 (inclusive).

h_i is an integer between 0 and 10^9 (inclusive).

The N coordinates (x_1, y_1), (x_2, y_2), (x_3, y_3), ..., (x_N, y_N) are all different.

The center coordinates and the height of the pyramid can be uniquely identified.

Input

Input is given from Standard Input in the following format:

N
x_1 y_1 h_1
x_2 y_2 h_2
x_3 y_3 h_3
:
x_N y_N h_N

Output

Print values C_X, C_Y and H representing the center coordinates and the height of the pyramid in one line, with spaces in between.

Sample Input 1

4
2 3 5
2 1 5
1 2 5
3 2 5

Sample Output 1

2 2 6

In this case, the center coordinates and the height can be identified as (2, 2) and 6.

Sample Input 2

2
0 0 100
1 1 98

Sample Output 2

0 0 100

In this case, the center coordinates and the height can be identified as (0, 0) and 100.

Note that C_X and C_Y are known to be integers between 0 and 100.

Sample Input 3

3
99 1 191
100 1 192
99 0 192

Sample Output 3

100 0 193

In this case, the center coordinates and the height can be identified as (100, 0) and 193.

Solution in Common Lisp (SBCL 1.1.14) (judge verdict: Wrong Answer)

(defvar *N* (read))
(defvar *MAX* (expt 10 9))

(defun calc (x-lst y-lst h-lst)
  (let ((tmp-h -1)
        (done nil))
    (dotimes (c-x 101)
      (dotimes (c-y 101)
        (dotimes (n *N*)
          (let* ((x (nth n x-lst))
                 (y (nth n y-lst))
                 (h (+ (nth n h-lst) (abs (- c-x x)) (abs (- c-y y)))))
            (when (/= h 0)
              (setq tmp-h h)
              (return-from nil))))
        (setq done t)
        (dotimes (n *N*)
          (let ((r (max (- tmp-h (abs (- c-x (nth n x-lst))) (abs (- c-y (nth n y-lst)))) 0)))
            (when (/= (nth n h-lst ) r)
              (setq done nil))))
        (when done
          (format t "~a ~a ~a" c-x c-y tmp-h)
          (return-from calc nil))))))

(defun main ()
  (let ((x-lst (list nil))
        (y-lst (list nil))
        (h-lst (list nil)))
    (loop repeat *N*
          do (progn
               (push (read) x-lst)
               (push (read) y-lst)
               (push (read) h-lst)))
    (setq x-lst (cdr (reverse x-lst)))
    (setq y-lst (cdr (reverse y-lst)))
    (setq h-lst (cdr (reverse h-lst)))
    (let ((count 0)
          (size (length h-lst)))
      (dolist (x h-lst)
        (when (= x 0)
          (incf count)))
      (if (= count size)
          (format t "0 0 1~%")
          (calc x-lst y-lst h-lst)))))

(main)