There are N electrons present in the coordinate plane. For each electron, you have been given three values \(X_i, Y_i\) and \(K_i\), where \(X_i\) and \(Y_i\) denotes X coordinate and Y coordinates of electron in the plane and \(K_i\) denotes the self - potential energy of \(i^{th}\) electron if other electron weren't present in the plane. You have to calculate potential energy of this system of electrons which is given by following formula: \(\sum_{i=1}^{i=N} \sum_{j=1}^{j=N} K_i * K_j * DIST(i,j)\)
\(DIST(i,j)\) denotes floor of euclidean distance between \(i^{th}\) and \(j^{th}\) electron. That is, \(DIST(i,j) = \lfloor \sqrt {(X_{i}-X_{j})^{2} + (Y_{i}-Y_{j})^{2}} \rfloor\) where \( \lfloor \rfloor\) denotes floor function.

Since electrons are very small in size, there can be more than one electron present at a point.

INPUT:
First line will consists of integer N denoting total number of electrons. Next N lines will consists of three integers \(X_i, Y_i, K_i\).

OUTPUT:
Output potential energy of this system of electrons. Since output can be large print it modulo \(10^9+7\).

CONSTRAINTS:
\(1 \le N \le 10^6\)
\(1 \le X_i, Y_i, K_i \le 500\)