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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val N = readLine()!!.toInt()
    val xyh = mutableListOf<Triple<Int, Int, Int>>()
    (1..N).forEach {
        val (x, y, h) = readLine()!!.split(" ").map { it.toInt() }
        xyh.add(Triple(x, y, h))
    }

    (0..100).forEach { cx ->
        (0..100).forEach { cy ->
            fun actualHeight(x: Int, y: Int, h: Int): Int {
                return Math.abs(x - cx) + Math.abs(y - cy) + h
            }

            val estimates = mutableListOf<Int>()
            val boundaries = mutableListOf<Int>()
            (0..(N - 1)).forEach {
                val (x, y, h) = xyh[it]
                if (h != 0) {
                    estimates.add(actualHeight(x, y, h))
                } else {
                    boundaries.add(actualHeight(x, y, 0))
                }
            }
            val h = estimates[0]
            var unique = true
            estimates.forEach {
                unique = unique && it == h
            }
            var valid = true
            boundaries.forEach {
                if (h > it) {
                    valid = false
                }
            }
            if (unique && h >= 1 && valid) {
                print(cx)
                print(' ')
                print(cy)
                print(' ')
                print(h)
                println("")
                return
            }
        }
    }
    println("Something is wrong")
}