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 (Python):
def main(sample_file = ''):

    """ convenient functions
    
    
    
    
    
    """

    """convenient decorator
    
    
        
        
        
        
        
        
        
        
        
        
    """
    
    
    import sys
    sys.setrecursionlimit(10**7)
    from itertools import accumulate, combinations, permutations, product 
    
    from math import factorial, ceil, floor, sqrt
    def factorize(n):
        """return the factors of the Arg and count of each factor
        
        Args:
            n (long): number to be resolved into factors
        
        Returns:
            list of tuples: factorize(220) returns [(2, 2), (5, 1), (11, 1)]
        """
        fct = []  
        b, e = 2, 0  
        while b * b <= n:
            while n % b == 0:
                n = n // b
                e = e + 1
            if e > 0:
                fct.append((b, e))
            b, e = b + 1, 0
        if n > 1:
            fct.append((n, 1))
        return fct
    def combinations_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        
        if n < 0 or r < 0:
            raise Exception('combinations_count(n, r) not defined when n or r is negative')
        if n - r < r: r = n - r
        if r < 0: return 0
        if r == 0: return 1
        if r == 1: return n
        numerator = [n - r + k + 1 for k in range(r)]
        denominator = [k + 1 for k in range(r)]
        for p in range(2,r+1):
            pivot = denominator[p - 1]
            if pivot > 1:
                offset = (n - r) % p
                for k in range(p-1,r,p):
                    numerator[k - offset] /= pivot
                    denominator[k] /= pivot
        result = 1
        for k in range(r):
            if numerator[k] > 1:
                result *= int(numerator[k])
        return result
    def combinations_with_replacement_count(n, r):
        """Return the number of selecting r pieces of items from n kinds of items allowing individual elements to be repeated more than once.
        
        Args:
            n (long): number
            r (long): number
        
        Raises:
            Exception: not defined when n or r is negative
        
        Returns:
            long: number
        """
        if n < 0 or r < 0:
            raise Exception('combinations_with_replacement_count(n, r) not defined when n or r is negative')
        elif n == 0:
            return 1
        else:
            return combinations_count(n + r - 1, r)
    from bisect import bisect_left, bisect_right
    from collections import deque, Counter, defaultdict 
    from heapq import heapify, heappop, heappush, heappushpop, heapreplace,nlargest,nsmallest 
    from copy import deepcopy, copy 
    import operator
    from operator import itemgetter 
    
    
    from functools import reduce, lru_cache
    def chmin(x, y):
        """change minimum
        if x > y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current minimum value
            y (long): potential minimum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x > y:
            x = y
            return (x, True)
        else:
            return (x, False)
    def chmax(x, y):
        """change maximum
        if x < y, x = y and return (x, True).
        convenient when solving problems of dp[i]
        
        Args:
            x (long): current maximum value
            y (long): potential maximum value
        
        Returns:
            (x, bool): (x, True) when updated, else (x, False)
        """
        if x < y:
            x = y
            return (x, True)
        else:
            return (x, False)

    from fractions import gcd 
    def gcds(numbers):
        return reduce(gcd, numbers)
    def lcm(x, y):
        return (x * y) // gcd(x, y)
    def lcms(numbers):
        return reduce(lcm, numbers, 1)
    def make_divisors(n, reversed=False):
        """create list of divisors
        
        Args:
            number (int): number from which list of divisors is created
            reversed (bool, optional): ascending order if False. Defaults to False.
        
        Returns:
            list: list of divisors
        """
        divisors = set()
        for i in range(1, int(n**0.5)+1):
            if n % i == 0:
                divisors.add(i)
                divisors.add(n//i)
        return sorted(list(divisors),reverse=reversed)
    
    
    
    INF = 10 ** 18
    MOD = 10 ** 9 + 7
    modpow = lambda a, n, p = MOD: pow(a, n, p) 
    def modinv(a, p = MOD):
        
        
        return modpow(a, p-2, p)
    def modinv_list(n, p = MOD):
        if n <= 1:
            return [0,1][:n+1]
        else:
            inv_t = [0,1]
            for i in range(2, n+1):
                inv_t += [inv_t[p % i] * (p - int(p / i)) % p]
            return inv_t
    def modfactorial_list(n, p = MOD):
        if n == 0:
            return [1]
        else:
            l = [0] * (n+1)
            tmp = 1
            for i in range(1, n+1):
                tmp = tmp * i % p
                l[i] = tmp
            return l
    def modcomb(n, k, fac_list = [], p = MOD):
        
        
        from math import factorial
        if n < 0 or k < 0 or n < k: return 0
        if n == 0 or k == 0: return 1
        if len(fac_list) <= n:
            a = factorial(n) % p
            b = factorial(k) % p
            c = factorial(n-k) % p
        else:
            a = fac_list[n]
            b = fac_list[k]
            c = fac_list[n-k]
        return (a * modpow(b, p-2, p) * modpow(c, p-2, p)) % p
    def modadd(a, b, p = MOD):
        return (a + b) % MOD
    def modsub(a, b, p = MOD):
        return (a - b) % p
    def modmul(a, b, p = MOD):
        return ((a % p) * (b % p)) % p
    def moddiv(a, b, p = MOD):
        return modmul(a, modpow(b, p-2, p))

    class UnionFindTree:
        """union find tree class
        TODO: fix this description...
        how to use (example):
        >>  uf = UnionFindTree(N) 
        >>  if uf.find_root(a) == uf.find_root(b):
        >>      do something
        >>  else:
        >>      do something
        >>      uf.unite(a, b)
        """
        def __init__(self, N):
            self.root = [-1] * (N+1)
            self.rank   = [0]  * (N+1)
            self.connected_num = [1] * (N+1)
    
        def find_root(self,x):
            root = self.root
            while root[x] != -1:
                x = root[x]
            return x
    
        def unite(self,x,y):
            root = self.root
            rank = self.rank
            connected_num = self.connected_num
            find_root = self.find_root
    
            rx = find_root(x)
            ry = find_root(y)
            if rx != ry:
                if rank[rx] < rank[ry]:
                    root[rx] = ry
                    rx,ry = ry,rx
                else:
                    if rank[rx] == rank[ry]:
                        rank[rx] += 1
                    root[ry] = rx       
                connected_num[rx] += connected_num[ry]

    
    
    
    
    

    def BellmanFord(N, M, ABC, vertex_start, vertex_end, value_if_inf = -1, find_shortest = False):
        """to calculate furthest or shortest length between vertex_start and vertex_end using BellmanFord algorithm
        
        Args:
            N (int): number of vertices
            M (int): number of edges
            ABC (list): [(ai, bi, ci) for _ in range(N)] where i-th edge is directed from vertex ai to vertex bi and the length is ci 
            vertex_start (int): start vertex. usually use 0.
            vertex_end (int): end vertex. usually use N-1.
            value_if_inf (int or string as you like, optional): value you want when the furthest (or shortest) distance is infinite (or -infinite). Defaults to -1.
            find_shortest (bool, optional): choose False to find furthest path. Defaults to False.
        
        Returns:
            int or string: normally int (but can be str if you set value_if_inf to str)
            
        Example:
                N, M, P = R()
                ABC = [R() for _ in range(M)]
                ABC = [(a-1, b-1, c-P) for a, b, c in ABC]
                print(BellmanFord(N, M, ABC, 0, N-1, value_if_inf = 'inf'))

        """

        def make_reachable_list(N, M, ABC, vertex_start, vertex_end):
            reachable_to_direct = defaultdict(list)
            reachable_from_direct = defaultdict(list)
            reachable_from_start = [False] * N
            reachable_to_end = [False] * N
            reachable_from_start[vertex_start] = True
            reachable_to_end[vertex_end] = True
            reachable_from_both_sides = [False] * N
            dfs_from_start = []
            dfs_to_end = []
            for a, b, c in ABC:
                reachable_to_direct[a].append(b)
                reachable_from_direct[b].append(a)
                if a == vertex_start:
                    dfs_from_start.append(b)
                    reachable_from_start[b] = True
                if b == vertex_end:
                    dfs_to_end.append(a)
                    reachable_to_end[a] = True
            while dfs_from_start:
                v = dfs_from_start.pop()
                for i in reachable_to_direct[v]:
                    if not reachable_from_start[i]:
                        reachable_from_start[i] = True
                        dfs_from_start.append(i)
            while dfs_to_end:
                v = dfs_to_end.pop()
                for i in reachable_from_direct[v]:
                    if not reachable_to_end[i]:
                        reachable_to_end[i] = True
                        dfs_to_end.append(i)
            for i in range(N):
                reachable_from_both_sides[i] = reachable_from_start[i] and reachable_to_end[i]
            return reachable_from_both_sides
        
        reachable_from_both_sides = make_reachable_list(N, M, ABC, vertex_start, vertex_end)
        
        if find_shortest:
            dist = [INF for i in range(N)]
        else:
            dist = [-INF for i in range(N)]
        
        dist[vertex_start] = 0
        for i in range(N):
            updated = False
            for a, b, c in ABC:
                if not reachable_from_both_sides[a]:
                    continue
                elif find_shortest:
                    update_condition = dist[a] + c < dist[b]
                else:
                    update_condition = dist[a] + c > dist[b]
                if dist[a] != INF and update_condition:
                    dist[b] = dist[a] + c
                    updated = True
                    if i == N-1:
                        return value_if_inf
            if not updated:
                break
        return dist[vertex_end]

    """ initialize variables and set inputs
    
        
        
    
        
        
        
        
        
        
        
    
        
        
        
        
    
        
        
    """

    
    r = lambda: sys.stdin.readline().strip()
    r_int = lambda: int(r())
    R = lambda: list(map(int, r().split()))
    Rmap = lambda: map(int, r().split())
    Rfloat = lambda: list(map(float, r().split()))
    Rtuple = lambda: tuple(map(int, r().split()))

    """ how to treat input
    
    
    
    
    
    
    
    """

    
    if sample_file:
        sys.stdin = open(sample_file)
        
    
    

    N = r_int()
    XYH = [R() for _ in range(N)]
    XYH.sort(key=itemgetter(2), reverse=True)
    for s in range(101):
        for t in range(101):
            xans, yans = s, t
            for i, (x, y, h) in enumerate(XYH):
                if i == 0:
                    hans = h + abs(xans-x) + abs(yans-y)
                else:
                    if max(hans-abs(xans-x)-abs(yans-y), 0) != h:
                        break
            else:
                print(xans, yans, hans)
                return
    

    
    
    

    """memo: how to use defaultdict of list
    
    Dic = defaultdict(list)
    
    Dic[x].append(y)
    
    for k, v in Dic.items():
    """
    
    """memo: how to solve binary problems
    
    >>> a = 5
    >>> bin_str_a = format(a, '
    >>> print(bin_str_a)
    0b0101 
    """
    
    """memo: how to solve the problem
    creating simple test/answer
    greed
    simple dp
    graph
    """

if __name__ == '__main__':
    main()

Solution (Python):
N = int(input())
L = [tuple(map(int, input().split())) for _ in range(N)]

xx, yy, hh = next(l for l in L if l[2] >= 1)
for Cx in range(101):
    for Cy in range(101):
        H = hh + abs(xx - Cx) + abs(yy - Cy)
        for x, y, h in L:
            if h != max(H - abs(x - Cx) - abs(y - Cy), 0):
                break
        else:
            print(Cx, Cy, H)
            quit()

Solution (Python):






def get_H(Cx, Cy):
    for x, y, h in L:
        if h > 0:
            return abs(x - Cx) + abs(y - Cy) + h


def check_H(Cx, Cy, H):
    for x, y, h in L:
        if h != max(H - abs(x - Cx) - abs(y - Cy), 0):
            return False
    return True


N = int(input())

L = [(list(map(int, input().split()))) for _ in range(N)]

for Cx in range(101):
    for Cy in range(101):
        H = get_H(Cx, Cy)
        if check_H(Cx, Cy, H):
            print('{} {} {}'.format(Cx, Cy, H))
            exit(0)

Solution (Python):
N=int(input())
xyh=[list(map(int,input().split()[:3])) for _ in range(N)]


ax, ay, ah = list(filter(lambda x: x[2], xyh))[0]

for x in range(101):
    for y in range(101):
        H=ah+abs(ax-x)+abs(ay-y)
        if all(max(H-abs(t[0]-x)-abs(t[1]-y),0) == t[2] for t in xyh):
            print(x,y,H)

Solution (Python):
def resolve():
    n = int(input())
    xyh = list(list(map(int, input().split())) for _ in range(n))
    px, py, ph = [[x, y, h] for x, y, h in xyh if h > 0][0]
    for cx in range(101):
        for cy in range(101):
            H = ph + abs(cx - px) + abs(cy - py)
            if all(hi == max(H - abs(cx - xi) - abs(cy - yi), 0) for xi, yi, hi in xyh):
                return " ".join([str(cx), str(cy), str(H)])


if __name__ == "__main__":
    print(resolve())

Solution (Python):
N = int(input())
L = [tuple(map(int, input().split())) for _ in range(N)]

def get_H(Cx, Cy):
    for x, y, h in L:
        if h == 0:
            continue
        H = h + abs(x - Cx) + abs(y - Cy)
        if H >= 1:
            return H

def check(Cx, Cy, H):
    for x, y, h in L:
        if h != max(H - abs(x - Cx) - abs(y - Cy), 0):
            return False
    return True

for Cx in range(101):
    for Cy in range(101):
        H = get_H(Cx, Cy)
        if check(Cx, Cy, H):
            print(Cx, Cy, H)
            quit()

Solution (Python):
N = int(input())
xyh = [list(map(int, input().split())) for _ in range(N)]

idx_flag = True

for i in range(N):
  if xyh[i][2] > 0:
    idx_flag = False
    idx = i
    break

if idx_flag:
  H = 1
  for i in range(101):
    for j in range(101):
      flag = True
      for k in range(N):
        cnt = 1 - abs(i-xyh[k][0]) - abs(j-xyh[k][1])
        if cnt > 0:
          flag = False
      if flag:
        print(i, j, H)
        exit(0)

for i in range(101):
  for j in range(101):
    flag = True
    h = abs(i-xyh[idx][0]) + abs(j-xyh[idx][1]) + xyh[idx][2]
    for k in range(N):
      cnt = abs(i-xyh[k][0]) + abs(j-xyh[k][1]) + xyh[k][2]
      if xyh[k][2] == 0:
        if cnt > h:
          continue
      if h != cnt:
        flag = False
    if flag:
      print(i, j, h)
      exit(0)

Solution (Python):
n = int(input())

x = [0 for i in range(n)]
y = [0 for i in range(n)]
h = [0 for i in range(n)]

k = 0

for i in range(n):
    x[i], y[i], h[i] = map(int, input().split())
    if h[i] > 0:
        k = i

ansx = -1
ansy = -1
ansh = -1

for cx in range(101):
    for cy in range(101):
        H = h[k] + abs(x[k] - cx) + abs(y[k] - cy)
        flag = True
        for i in range(n):
            if max(H - abs(x[i] - cx) - abs(y[i] - cy), 0) != h[i]:
                flag = False
                break
        if flag:
            ansx = cx
            ansy = cy
            ansh = H
            break
    if ansx >= 0:
        break

print(ansx, ansy, ansh)

Solution (Python):
n = int(input())
x, y, h = [], [], []
for _ in range(n):
    a, b, c = map(int, input().split())
    x.append(a)
    y.append(b)
    h.append(c)


for cx in range(101):
    for cy in range(101):
        for i in range(n):
            ch = h[i] + abs(x[i] - cx) + abs(y[i] - cy)
            if all(h[j] == max(ch - abs(x[j] - cx) - abs(y[j] - cy), 0) for j in range(n)):
                print(cx, cy, ch)
                exit()

Solution (Python):
n=int(input())
d=[]
for i in range(n):
    a,b,c=map(int,input().split())
    d.append((a,b,c))
    if c!=0:
        x,y,h=a,b,c

for i in range(101):
    for j in range(101):
        p=abs(i-x)+abs(j-y)+h
        for a,b,c in d:
            if (c==0 and p-abs(i-a)-abs(j-b)<1) or (c==(p-abs(i-a)-abs(j-b))):
                pass
            else:
                p=-1
                break
        if p!=-1:
            print(i,j,p)
            exit()

Solution (Python):
n=int(input())
d=[]
for i in range(n):
    a,b,c=map(int,input().split())
    d.append((a,b,c))
    if c!=0:
        x=a
        y=b
        h=c

for i in range(101):
    for j in range(101):
        p=abs(i-x)+abs(j-y)+h
        for a,b,c in d:
            if (c==0 and p-abs(i-a)-abs(j-b)<1) or (c==(p-abs(i-a)-abs(j-b))):
                pass
            else:
                p=-1
                break
        if p!=-1:
            print(i,j,p)
            exit()

Solution (Python):
A=abs
_,*p=[list(map(int,t.split()[::-1]))for t in open(0)]
h,y,x=max(p)
r=range(101)
for i in r:
 for j in r:H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for u,t,s in p))

Solution (Python):
n=int(input())
xyh=[list(map(int,input().split())) for _ in range(n)]
for x,y,h in xyh:
    if h>0:
        sx=x
        sy=y
        sh=h
        break
for i in range(101):
    for j in range(101):
        th=abs(i-sx)+abs(j-sy)+sh
        for x,y,h in xyh:
            if h!=max(th-abs(i-x)-abs(j-y),0):
                break
        else:
            break
    else:
        continue
    break
print(i,j,th)

Solution (Python):
n=int(input())
xyh=[list(map(int,input().split())) for _ in range(n)]
for x,y,h in xyh:
    if h>0:
        sx=x
        sy=y
        sh=h
for i in range(101):
    for j in range(101):
        th=abs(i-sx)+abs(j-sy)+sh
        for x,y,h in xyh:
            if h!=max(th-abs(i-x)-abs(j-y),0):
                break
        else:
            break
    else:
        continue
    break
print(i,j,th)

Solution (Python):
n=int(input())

L=[[{0}for i in range(0,101)]for q in range(0,101)]
cnt=0

for inp in range(n):
    x,y,h=map(int,input().split())
    if h != 0:
        cnt+=1
        for i in range(0,101):
            for q in range(0,101):
                L[i][q].add(h+abs(x-i)+abs(y-q))
    else:
        L[x][y].add(-1)

if cnt==1:
    for i in range(101):
        for q in range(101):
            if L[i][q]=={0,1}:
                print(str(i)+" "+str(q)+" "+"1")
                break
else:  
    for i in range(101):
        for q in range(101):
            if len(L[i][q])==2 and max(L[i][q])>0:
                print(str(i)+" "+str(q)+" "+str(max(L[i][q])))

Solution (Python):
N=int(input())
d={}
for i in range(N):
	x,y,h=map(int,input().split())
	d[tuple([x,y])]=h

for i in range(101):
	for j in range(101):
		h=-1
		for p in d:
			if d[p]!=0:
				h=max(h,abs(p[0]-i)+abs(p[1]-j)+d[p])
		f=True
		for p in d:
			if d[p]!=max(0,h-abs(p[0]-i)-abs(p[1]-j)):
				f=False
				break
		if f==True:
			print(i,j,h)

Solution (Python):
N = int(input())

L = []
for i in range(N):
    x, y, h = map(int, input().split())
    L.append([x, y, h])
    if h != 0:
        idx = i


for i in range(101):
    for j in range(101):
        H = L[idx][2] + abs(L[idx][0]-i) + abs(L[idx][1]-j)
        for k in range(N):
            if L[k][2] == max(H - abs(L[k][0]-i) - abs(L[k][1]-j), 0):
                pass
            else:
                break
            if k == N-1:
                ansx = i
                ansy = j
                ansh = H

print(ansx, ansy, ansh)

Solution (Python):
N = int(input())
P = [list(map(int, input().split())) for i in range(N)]
C = [[0]*101 for i in range(101)]
P.sort(key=lambda x:x[2], reverse=True)
for X in range(101):
  for Y in range(101):
    tmp1 = -1
    flg = 0
    for i in range(N):
      x,y,h = P[i]
      if h != 0 and tmp1 == -1:
        tmp1 = abs(X-x)+abs(Y-y)+h
      elif tmp1 != -1:
        tmp2 = abs(X-x)+abs(Y-y)+h
        if h != 0: 
          if tmp1 != tmp2:
            flg = 1
            break
        if h == 0:
          if tmp1 > tmp2:
            flg = 1
            break
    if flg == 0:
      print(X, Y, tmp1)        
      exit()

Solution (Python):
A=abs
_,*p=[list(map(int,t.split()[::-1]))for t in open(0)]
h,y,x=sorted(p)[-1]
r=range(101)
for i in r:
 for j in r:H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for u,t,s in p))

Solution (Python):



import sys
import math
import bisect
sys.setrecursionlimit(1000000000)
from heapq import heappush, heappop
from collections import defaultdict
from itertools import accumulate
from collections import Counter
from collections import deque
from operator import itemgetter
from itertools import permutations
mod = 10**9 + 7
inf = float('inf')
def I(): return int(sys.stdin.readline())
def LI(): return list(map(int,sys.stdin.readline().split()))

n = I()
xyh = [LI() for _ in range(n)]
maxh = 0
for x,y,h in xyh:
    maxh = max(maxh,h)
for H in range(maxh,maxh+201):
    for cx in range(101):
        for cy in range(101):
            for x,y,h in xyh:
                if h != max(H-abs(x-cx)-abs(y-cy),0):
                    break
            else:
                print(cx,cy,H)
                quit()

Solution (Python):
def c_pyramid():
    N = int(input())
    Pos = [[int(i) for i in input().split()] for j in range(N)]
    
    x, y, h = sorted(Pos, key=lambda x: x[2])[-1]
    
    for cx in range(101):
        for cy in range(101):
            
            height = h + abs(x - cx) + abs(y - cy)  
            if all(h_i == max(height - abs(x_i - cx) - abs(y_i - cy), 0)
                   for x_i, y_i, h_i in Pos):
                return '{} {} {}'.format(cx, cy, height)  
    return None

print(c_pyramid())

Solution (Python):
A=abs
_,*p=[list(map(int,t.split()))for t in open(0)]
for t in p:
 if t[2]:x,y,h=t
r=range(101)
for i in r:
 for j in r:H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for s,t,u in p))

Solution (Python):
A=abs
_,*p=[list(map(int,t.split()))for t in open(0)]
for t in p:
 if t[2]:x,y,h=t
for I in range(10201):j,i=I//101,I%101;H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for s,t,u in p))

Solution (Python):
N = int(input())
XYH = [list(map(int, input().split())) for _ in range(N)]

for cx in range(101):
	for cy in range(101):
		ch = None
		for x, y, h in XYH:
			if 0 < h:
				ch = h + abs(x - cx) + abs(y - cy)
				if 0 < ch:
					break
		else:
			continue
		for x, y, h in XYH:
			th = max(0, ch - abs(x - cx) - abs(y - cy))
			if th != h:
				break
		else:
			print(cx, cy, ch)
			exit()

Solution (Python):
from operator import itemgetter
import sys
input = sys.stdin.readline
def inpl(): return list(map(int, input().split()))

N = int(input())
Q = sorted([inpl() for _ in range(N)], key=itemgetter(2), reverse=True)

for cx in range(101):
    for cy in range(101):
        ch = abs(cx - Q[0][0]) + abs(cy - Q[0][1]) + Q[0][2]
        for x, y, h in Q:
            if h != max(ch - abs(x-cx) - abs(y-cy), 0):
                break
        else:
            print(cx, cy, ch)

Solution (Python):
import sys

stdin = sys.stdin

sn = lambda : stdin.readline().rstrip()
an = lambda : list(map(int, stdin.readline().split()))
ni = lambda : int(sn())

n = ni()
xyz = [0] * n
for i in range(n):
  xyz[i] = an()

xyz.sort(key = lambda x: x[2])

sx, sy, sh = xyz[-1]
for Cy in range(101):
  for Cx in range(101):
    H = sh + abs(sx - Cx) + abs(sy - Cy)
    if all(h == max(H - abs(x - Cx) - abs(y - Cy), 0) for x, y, h in xyz):
      print(Cx, Cy, H)
      exit()

Solution (Python):
A=abs
_,*p=[list(map(int,t.split()))for t in open(0)]
x,y,h=[t for t in p if t[2]][0]
for I in range(10201):j,i=I//101,I%101;H=h+A(x-j)+A(y-i);print(*(j,i,H)*all(u==max(H-A(s-j)-A(t-i),0)for s,t,u in p))

Solution (Python):
N = int(input())
XYH = [list(map(int, input().split())) for _ in range(N)]

for x0 in range(101):
    for y0 in range(101):
        a = -1
        ok = True
        for x, y, h in XYH:
            if h == 0:
                continue
            if a == -1:
                a = abs(x-x0) + abs(y-y0) + h
                continue
            if a != abs(x-x0) + abs(y-y0) + h:
                ok = False
                break
        for x, y, h in XYH:
            if h != max(a- abs(x0-x) - abs(y0-y), 0):
                ok = False
        if ok:
            print(x0, y0, a)
            break
    if ok:
        break

Solution (Python):
N = int(input())

xyh = [list(map(int,input().split())) for _ in range(N)]
xyh.sort(key=lambda x:-x[2])

def ok(cx,cy,H):
    res = True
    for i in range(1,N):
        x,y,h = xyh[i]
        if max(H-abs(x-cx)-abs(y-cy),0) != h:
            res = False
            break
    return res

x,y,h = xyh[0]
for cx in range(101):
    for cy in range(101):
        H = h+abs(x-cx)+abs(y-cy)
        if ok(cx,cy,H):
            ans = '{} {} {}'.format(cx,cy,H)

print(ans)

Solution (Python):
import sys
import heapq
from operator import itemgetter
from collections import deque, defaultdict
from bisect import bisect_left, bisect_right
input = sys.stdin.readline
sys.setrecursionlimit(10 ** 7)

def sol():
    N = int(input())
    points = [tuple(map(int, input().split())) for _ in range(N)]
    points.sort(key=itemgetter(2), reverse=True)

    for cx in range(101):
        for cy in range(101):
            bx, by, bh = points[0]
            H = bh + abs(cx - bx) + abs(cy - by)
            for x, y, h in points:
                nowH = max(H - abs(cx - x) - abs(cy - y), 0)
                if h != nowH:
                    break
            else:
                print(cx, cy, H)
                return

sol()

Solution (Python):
def main():
    N = int(input())
    
    p = []
    isFound = False
    for _ in range(N):
        x, y, h = map(int, input().split())
        p.append([x, y, h])
        if not isFound and h > 0:
            ref = [x, y, h]
            isFound = True
    

    for cx in range(0, 100+1):
        for cy in range(0, 100+1):
            isCenter = True
            H = ref[2] + abs(ref[0]-cx) + abs(ref[1]-cy)
            for x, y, h in p:
                if h > 0:
                    Hp = h + abs(x-cx) + abs(y-cy)
                    if Hp != H:
                        isCenter = False
                        break
                else:
                    if (H - abs(x-cx) - abs(y-cy)) > 0:
                        isCenter = False
                        break
            if isCenter:
                return [cx, cy, H]
    return [-1,-1,-1]

if __name__ == '__main__':
    output = main()
    print(' '.join(map(str, output)))

Solution (Python):

import sys


def solve(N: int, x: "List[int]", y: "List[int]", h: "List[int]"):

    
    ansx = -1
    ansy = -1
    ansh = -1

    
    
    ix = h.index(max(h))

    for cx in range(101):
        for cy in range(101):
            H = h[ix] + abs(x[ix]-cx) + abs(y[ix]-cy)
            f = True
            for i in range(N):
                if(h[i] > 0 and H-h[i] != abs(x[i]-cx) + abs(y[i]-cy)):
                    f = False
                if(h[i] == 0 and H > abs(x[i]-cx) + abs(y[i]-cy)):
                    f = False
            if(f):
                ansx = cx
                ansy = cy
                ansh = H
        

    print(ansx, ansy, ansh)
    return



def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  
    x = [int()] * (N)  
    y = [int()] * (N)  
    h = [int()] * (N)  
    for i in range(N):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
        h[i] = int(next(tokens))
    solve(N, x, y, h)

if __name__ == '__main__':
    main()

Solution (Python):
from collections import Counter
N = int(input())
L = [list(map(int, input().split())) for _ in range(N)]

for cx in range(101):
  for cy in range(101):
    l0 = [abs(cx - x) + abs(cy - y) for x, y, h in L if h == 0]
    m = min(l0) if l0 else float('inf')
    c = Counter(h + abs(cx - x) + abs(cy - y) for x, y, h in L if h != 0)
    if len(c) == 1 and c.most_common()[0][0] <= m:
      print(cx, cy, c.most_common()[0][0])
      exit()

Solution (Python):
N = int(input())

x = [0] * N
y = [0] * N
h = [0] * N

for i in range(N):
    xyh = list(map(int, input().split()))
    x[i] = xyh[0]
    y[i] = xyh[1]
    h[i] = xyh[2]
    if xyh[2] != 0:
        Cx = xyh[0]
        Cy = xyh[1]
        CH = xyh[2]

for i in range(101):
    for j in range(101):
        flag = True
        H = CH + abs(i - Cx) + abs(j - Cy)
        for k in range(N):
            if h[k] != max(H - abs(i - x[k]) - abs(j - y[k]), 0):
                flag = False
                break
        if flag:
            print(i, j, H)