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: Wrong Answer)

fun main(args: Array<String>) {
    val N = readLine()!!.toInt()

    val x = LongArray(N) { 0L }
    val y = LongArray(N) { 0L }
    val h = LongArray(N) { 0L }

    for (i in 0 until N) {
        val (X, Y, H) = readLine()!!.split(" ").map { it.toLong() }
        x[i] = X
        y[i] = Y
        h[i] = H
    }

    fun check(cx: Long, cy: Long, H: Long): Boolean {
        if (h.max()!! > H) return false

        for (i in x.indices) {
            val dh = H - h[i]
            if (dh != Math.abs(x[i] - cx) + Math.abs(y[i] - cy) && h[i] != 0L) {
                return false
            }
        }

        return true
    }

    for (a in 0..100) {
        for (b in 0..100) {
            val dx = Math.abs(a - x[0])
            val dy = Math.abs(b - y[0])

            val ch = h[0] + dx + dy

            if (check(a.toLong(), b.toLong(), ch)) {
                println("$a $b $ch")

                return
            }
        }
    }
}