import sys

# sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()

# dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
inf = (1 << 63)-1
# inf = (1 << 31)-1
md = 10**9+7
# md = 998244353

def binary_search(l, r, minimize):
    if minimize: l -= 1
    else: r += 1
    while l+1 < r:
        m = (l+r)//2
        if ok(m) ^ minimize: l = m
        else: r = m
    if minimize: return r
    return l

def ok(m):
    def move(i, j):
        x1, y1, t1 = xyt[i]
        x2, y2, t2 = xyt[j]
        if t1 == t2:
            if (x2-x1)**2+(y2-y1)**2 > m: return False
        else:
            R = x1**2+y1**2
            r = x2**2+y2**2
            if R+r-m < 0:return True
            if (R+r-m)**2 > 4*R*r:return False
        return True

    st = [0]
    vis = [0]*n
    vis[0] = 1
    while st:
        i = st.pop()
        for j in range(n):
            if vis[j]: continue
            if not move(i, j): continue
            if j == n-1: return True
            vis[j] = 1
            st.append(j)
    return False

n = II()
xyt = LLI(n)

ans = binary_search(0, 3200000005, True)
print(ans)