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.

Examples

Input

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


Output

2 2 6


Input

2
0 0 100
1 1 98


Output

0 0 100


Input

3
99 1 191
100 1 192
99 0 192


Output

100 0 193
import java.util.*;
 
public class Main{
    static int N;
    static int[][] x;
    static int cx;
    static int cy;
    public static void main(String args[]){
       Scanner sc = new Scanner(System.in); 
       
        N = sc.nextInt();
        x = new int[3][N];
       for(int i = 0; i < N; i++){
           x[0][i] = sc.nextInt();
           x[1][i] = sc.nextInt();
           x[2][i] = sc.nextInt();
       }
       sc.close();

       for(int i = 0; i <= 100; i++){
            loop: for(int j = 0; j <= 100; j++){
                cx = i;
                cy = j;
                int H = decide_h();
                for(int k = 0; k < N; k++){
                    if(Math.max(H - Math.abs(x[0][k] - cx) - Math.abs(x[1][k] - cy), 0) != x[2][k]){
                        continue loop;
                    }
                    if(k == N-1){
                        System.out.println(cx + " " + cy + " " + H);
                        break;
                    }
                }
            }
       }
    }
    static int decide_h(){
        for(int l = 0; l < N; l++){
            if(x[2][l] > 0){
                return x[2][l] + Math.abs(x[0][l] - cx) + Math.abs(x[1][l] - cy);
            }
        }

        return 0;
    }
}