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 max(int a,int b){return a > b ? a:b;} 
int sortmax(int h[],int n);
int hantei(int Cx,int Cy,int H,int N,int x[],int y[],int h[]);

int main(){
    /*入力*/
    int N;
    int m =scanf("%d",&N);
    int x[N],y[N],h[N];
    for(int i = 0;i < N;i++){
        int l = scanf("%d%d%d",&x[i],&y[i],&h[i]);
    }

    /*hのうち一番高いところはどこか調べる*/
    int arraynumber = sizeof(h)/sizeof(h[0]);
    int maxh = sortmax(h,arraynumber);

/*各Cx,Cy,Hについて全ての観測値に整合するかどうかを調べる。もしそうなるのが合ったらそれを出力する*/
    int Cx,Cy,H;
    for(H = maxh;;H++){
        for(int Cx = 0;Cx <= 100;Cx++){
            for(int Cy = 0;Cy <=100;Cy++){
                int mark = hantei(Cx,Cy,H,N,x,y,h);//ここで判定。一致したら１を返す。
                if(mark == 1){
                    printf("%d %d %d\n",Cx,Cy,H);
                    return 0;
                }
            }
        }
    }
    return 0;
}

int sortmax(int h[],int n){
    for(int i = 0;i < n;i++){
            h[0] = max(h[0],h[i]);
        }
    return h[0];
}

int hantei(int Cx,int Cy,int H,int N,int x[],int y[],int h[]){
    for(int i = 0;i < N;i++){
        int cal = H - abs(x[i] - Cx) - abs(y[i] - Cy);
        if(h[i] != max(cal,0))return 0;
    }
    return 1;
}