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 C (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>
#include <stdlib.h>

int main()
{
    int n, x[100], y[100], h[100], i, j, k, H, flag;
    scanf("%d\n", &n);
    for (i=0; i<n; i++)
    {
        scanf("%d%d%d", &x[i], &y[i], &h[i]);
    }

    for (i=0; i<=100; i++)
    {
        for (j=0; j<=100; j++)
        {
            flag = 0;
            for (k=0; k<n; k++)
            {
                if (h[k]>0) {
                    if (flag == 0) {
                        H = h[k] + abs(i-x[k]) + abs(j-y[k]);
                        flag = 1;
                    } else {
                        if (H != h[k] + abs(i-x[k]) + abs(j-y[k]))
                        flag = 2;
                        break;
                    }
                }
            }
            for (k=0; k<n; k++)
            {
                if (h[k] == 0) {
                    if (H > h[k] + abs(i-x[k]) + abs(j-y[k]))
                    flag = 2;
                    break;
                }
            }
            if (flag == 1) {
                break;
            }
        } if (flag == 1) {
            break;
        }
    } if (flag == 1) {
        printf("%d %d %d\n", i, j, H);
    }
    return 0;
}