There are \(N\) huge stones in the field, located in points \(P_1, P_2, \ldots, P_N\) (not necessarily different). Their weights are positive integer numbers \(W_1, W_2, \ldots, W_N\).

You want to make a view on this field picturesque. To do this you should move these stones to the new points \(P'_1, P'_2, \ldots, P'_N\), such that these points are lying at some circle. Let's define the difficulty to make this as a real number equal to\(\sum\limits_{k=1}^N{dist(P_i, P'_i) \cdot W_i}\).

You want to find some circle with center in point \((X_0, Y_0)\) and radius \(R\) , such that the difficulty to make all stones lying on this circle as minimal as possible. Points \(P'_1, P'_2, \ldots, P'_N\) will be chosen optimally for your circle, you should find only the circle.

Input format

On the first line, you are given one integer number \(N\) (number of stones).
On the next \(N\) lines you are given \(3\) integer numbers \(X_i, Y_i, W_i\),coordinates of point \(P_i\) and weight of \(i\)-th stone.

Output format

Print \(3\) real numbers \(X_0, Y_0, R\) coordinates of the center of the optimal circle and its radius. This numbers should satisfy the conditions \(-10^6 \leq X_0, Y_0 \leq 10^6\) and \(0 \leq R \leq 4 \cdot 10^6\).

Constraints

\(N = 50000 \) in all test cases except sample test
\(P_i = (X_i, Y_i), -10^6 \leq X_i, Y_i \leq 10^6, 1 \leq W_i \leq 10^6\)

Note: The input data contains only 50 percent of the original test data. The other data will be added after the contest and the submissions will be rejudged.

Verdict and scoring
If numbers \(X_0, Y_0, R\) don't satisfy the required conditions you will get a Wrong Answer verdict. For each of the valid output points \(P'_1, P'_2, \ldots, P'_N\) will be generated, such that difficulty as minimum as possible.