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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program main
Implicit None
integer(8)::n,i,j,u,xa,ya,ha,hb,k,m
integer(8),allocatable::x(:),y(:),h(:)
	
	read *,n
	allocate(x(n),y(n),h(n))
	
	do i = 1,n
		read *,x(i),y(i),h(i)
	enddo
	
	i = 1
	do while(h(i) == 0)
		i = i +1
	enddo
	
	u = h(i);xa = x(i);ya = y(i)
	
	do k = 0,100
		do j = 0,100
			ha = abs(k - xa)+abs(j - ya) + u
			do m = i + 1,n
				hb = ha - abs(x(m) - k) - abs(y(m) - j)
				if(hb < 0) hb = 0
				if(hb /= h(m)) exit
				if(m == n)then
					print 101,k,j,ha
					stop
				endif
			enddo
		enddo
	enddo
	
101 format(i0,1xi0,1xi0)
end program main