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:
$1 \le N \le 10^6$
$1 \le X_i, Y_i, K_i \le 500$