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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function getLines(input){
	return input.split("\n").map((s)=>s.trim())
}
function parseLine(line){
	return line.split(" ").map((s)=>s.trim());
}
function parseLineToInt(line){
	return line.split(" ").map((s)=>parseInt(s.trim()));
}
// parameter "input" gets all data
function Main(input) {
	// the first line is assigned to input[0], the second line is assigned to input[1] similarly.	
	input = getLines(input).map(parseLineToInt);
	var n = input[0][0];
	input.shift()

	var calc = (e,i,j)=>(Math.abs(e[0]-i)+Math.abs(e[1]-j)+e[2])
	var verify = (e,H,i,j)=>{
		//console.log(e,H,i,j,(Math.max(H-Math.abs(e[0]-i)-Math.abs(e[1]-j),0)),e[2])
		return (Math.max(H-Math.abs(e[0]-i)-Math.abs(e[1]-j),0))==e[2]
	}
	var minx,miny,maxx,maxy;
	/*input.sort((a,b)=>a[0]-b[0]);
	minx=input[0][0];
	maxx=input[n-1][0];
	input.sort((a,b)=>a[1]-b[1]);
	miny=input[0][1];
	maxy=input[n-1][1];*/
	input.sort((a,b)=>a[2]-b[2])
	minx=0,miny=0,maxx=100,maxy=100;
	for (var i = minx; i <= maxx; i++) {
		for (var j = miny; j <= maxy; j++) {
			var h = -1;
			var go = false
			for (var k = 0; k <	n; k++) {
				if(h == -1){
					h = calc(input[k],i,j)
				//	console.log('---',h)
				}
				if(h<1 || !verify(input[k],h,i,j)){
					go = true
					break;
				}
				
				
			}
			if(!go){
				console.log([i,j,h].join(' '));
			}
		}

	}
	
}
// Don't edit this line!
//Main(require("fs").readFileSync(__dirname+'/in.txt', "utf8"));
Main(require('fs').readFileSync('/dev/stdin', 'utf8'));