#include <iostream>
#include <cstdio>
#include <algorithm>
#include <string>
#include <math.h>
#include <memory.h>
#include <vector>
using namespace std;
const int MAXN=105;
int xyh[MAXN][5],n;
int main(){
	cin>>n;
	int i,j,k,x,f,s,t;
	for(i=1;i<=n;i++)
		cin>>xyh[i][1]>>xyh[i][2]>>xyh[i][3];
	s=1;
	while(xyh[s][3]==0)s++;
	for(i=0;i<=100;i++){
		for(j=0;j<=100;j++){
			x=xyh[s][3]+abs(xyh[s][1]-i)+abs(xyh[s][2]-j);
			f=1;
			for(k=1;k<=n;k++){
				t=max(0,x-abs(xyh[k][1]-i)-abs(xyh[k][2]-j));
				if(xyh[k][3]!=t){
					f=0;break;
				}
			}
			if(f==1){printf("%d %d %d",i,j,x);return 0;}
		}
	}
	return 0;
}

### Prompt

Please provide a CPP coded solution to the problem described below:

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

### Response

```cpp
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <string>
#include <math.h>
#include <memory.h>
#include <vector>
using namespace std;
const int MAXN=105;
int xyh[MAXN][5],n;
int main(){
	cin>>n;
	int i,j,k,x,f,s,t;
	for(i=1;i<=n;i++)
		cin>>xyh[i][1]>>xyh[i][2]>>xyh[i][3];
	s=1;
	while(xyh[s][3]==0)s++;
	for(i=0;i<=100;i++){
		for(j=0;j<=100;j++){
			x=xyh[s][3]+abs(xyh[s][1]-i)+abs(xyh[s][2]-j);
			f=1;
			for(k=1;k<=n;k++){
				t=max(0,x-abs(xyh[k][1]-i)-abs(xyh[k][2]-j));
				if(xyh[k][3]!=t){
					f=0;break;
				}
			}
			if(f==1){printf("%d %d %d",i,j,x);return 0;}
		}
	}
	return 0;
}

```