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 12.16.1) (judge verdict: Wrong Answer)

//Don't have to see. start------------------------------------------
var read = require('readline').createInterface({
  input: process.stdin, output: process.stdout
});
var obj; var inLine = [];
read.on('line', function(input){inLine.push(input);});
read.on('close', function(){
  obj = init(inLine);
  console.error("\n");
  var start = Date.now();
  Main();
  var end = Date.now() - start;
  myerr("time : " + (end) + "ms");
  myerr("memory : " + Math.round(process.memoryUsage().heapTotal / 1024) + "KB");
});
function makeClone(obj){return JSON.parse(JSON.stringify(obj));}
function nextInt(){return myconv(next(),1);} function nextStrArray(){return myconv(next(),2);}
function nextIntArray(){return myconv(next(),4);} function nextCharArray(){return myconv(next(),6);}
function next(){return obj.next();} function hasNext(){return obj.hasNext();}
function init(input){  
  return {
    list : input, index : 0, max : input.length,
    hasNext : function(){return (this.index < this.max);},
    next : function(){if(this.hasNext()){return this.list[this.index++];}else{throw "ArrayIndexOutOfBoundsException ‚There is no more input";}}
  };
}
function myout(s){console.log(s);}
function myerr(s){console.error("debug:" + require("util").inspect(s,false,null));}
//param "no" is
//unknown or outlier : return i. 1: parseInt.
//2: split space. 4: split space and parseInt.
//6: split 1 character. 7: split 1 character and parseInt.
//8: join space. 9: join nextline. 0: join no character.
function myconv(i,no){try{switch(no){case 1:return parseInt(i);case 2:return i.split(" ");case 4:return i.split(" ").map(Number);case 6:return i.split("");case 7:return i.split("").map(Number);case 8:return i.join(" ");case 9:return i.join("\n");case 0:return i.join("");default:return i;}}catch(e){return i;}}

//Don't have to see. end------------------------------------------
function Main(){
  var N = nextInt();
  var max = 101;
  var dy = [-1,0,1,0];
  var dx = [0,-1,0,1];
  var list = new Array(max);
  var highList = new Array(max);
  var access = new Array(max);
  for(var i = 0; i < max; i++){
    list[i] = new Array(max).fill(0);
    highList[i] = new Array(max);
    access[i] = new Array(max).fill(false);
    for(var j = 0; j < max; j++){
      highList[i][j] = new Set();
    }
  }
  var check = new Array(N);
  for(var i = 0; i < N; i++){
    var tmp = nextIntArray();
    list[tmp[1]][tmp[0]] = tmp[2];
    //highList[tmp[1]][tmp[0]].add(tmp[2]);
    check[i] = [tmp[1], tmp[0]];
  }
  for(var i = 0; i < N; i++){
    if(list[check[i][0]][check[i][1]] != 0){
      bfs(check[i][0], check[i][1]);
    }
  }
  for(var i = 0; i < max; i++){
    for(var j = 0; j < max; j++){
      if(highList[i][j].size == 1){
        var output = Array.from(highList[i][j]);
        myout(j + " " + i + " " + output[0]);
        return;
      }
    }
  }
  var check2 = new Array(N);
  for(var i = 0; i < N; i++){
    check2[i] = check[i].join(":");
  }
  for(var i = 0; i < max; i++){
    for(var j = 0; j < max; j++){
      if(list[i][j] == 0 && check2.indexOf(i + ":" + j) == -1){
        myout(i + " " + j + " " + 1);
        return;
      }
    }
  }
  
  
  function bfs(y, x){
    for(var i = 0; i < max; i++){
      access[i] = new Array(max).fill(false);
    }
    access[y][x] = true;
    var queue = [[y, x, list[y][x]]];
    while(queue.length > 0){
      var now = queue.shift();
      var nowY = now[0];
      var nowX = now[1];
      var value = now[2];
      highList[nowY][nowX].add(value);
      for(var i = 0; i < dy.length; i++){
        var nextY = nowY + dy[i];
        var nextX = nowX + dx[i];
        if(nextY >= 0 && nextY < max && nextX >= 0 && nextX < max){
          if(!access[nextY][nextX]){
            access[nextY][nextX] = true;
            queue.push([nextY, nextX, value + 1]);
          }
        }
      }
    }
  }
}