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: Accepted)

(eval-when (:compile-toplevel :load-toplevel :execute)
  (defparameter OPT
    #+swank '(optimize (speed 3) (safety 2))
    #-swank '(optimize (speed 3) (safety 0) (debug 0)))
  #+swank (progn (ql:quickload '(:cl-debug-print :fiveam))
                 (shadow :run)
                 (use-package :fiveam)))
#+swank (cl-syntax:use-syntax cl-debug-print:debug-print-syntax)

;; BEGIN_INSERTED_CONTENTS
(defmacro split-ints-bind (vars string &body body)
  (let ((position (gensym))
        (s (gensym)))
    (labels ((expand (vars &optional init-pos)
               (if (null vars)
                   body
                   `((multiple-value-bind (,(car vars) ,position)
                         (parse-integer ,s :start ,(or init-pos position)
                                           :junk-allowed t)
                       ,@(when (null (cdr vars)) `((declare (ignore ,position))))
                       ,@(expand (cdr vars)))))))
      `(let ((,s ,string))
         (declare (string ,s))
         ,@(expand vars 0)))))

(defmacro define-int-types (&rest bits)
  `(progn
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "UINT~A" b)) () '(unsigned-byte ,b))) bits)
     ,@(mapcar (lambda (b) `(deftype ,(intern (format nil "INT~A" b)) () '(signed-byte ,b))) bits)))
(define-int-types 2 4 7 8 15 16 31 32 62 63 64)

(defmacro println (obj &optional (stream '*standard-output*))
  `(let ((*read-default-float-format* 'double-float))
     (prog1 (princ ,obj ,stream) (terpri ,stream))))

(defconstant +mod+ 1000000007)

;; Hauptteil

(defun main ()
  (let* ((n (read))
         (hxy-table (make-array n :element-type '(cons uint32 (cons uint32 uint32)))))
    (dotimes (i n)
      (split-ints-bind (x y h) (read-line)
        (setf (aref hxy-table i) (list h x y))))
    (setf hxy-table (sort hxy-table #'> :key #'car))
    (when (zerop (car (aref hxy-table 0)))
      (error "Huh?"))
    (dotimes (cx 101)
      (dotimes (cy 101)
        (loop with cand-height = most-positive-fixnum
              for i below n
              for (h x y) of-type (uint32 uint32 uint32) = (aref hxy-table i)
              do (if (zerop h)
                     (unless (<= cand-height (+ (abs (- x cx)) (abs (- y cy))))
                       (return))
                     (let ((must-height (+ h (abs (- x cx)) (abs (- y cy)))))
                       (when (< must-height 1)
                         (return))
                       (if (= cand-height most-positive-fixnum)
                           (setf cand-height must-height)
                           (unless (= cand-height must-height)
                             (return)))))
              finally (format t "~A ~A ~A~%" cx cy cand-height)
                      (return-from main))))))

#-swank(main)