Yuki is a grumpy girl and she always wants to make some noise.

One day, Yuki goes to the amusement ground in her university and sets \(n\) bombs. The \(i\)-th bomb set at the position \((x_i,y_i)\) has exploding radius \(r_i\) and lighting-cost \(t_i\), which means that Yuki needs to spend \(t_i\) seconds to config the bomb and make it exploded by remote control.

A bomb will explode **instantly** if it is in the exploding area (**including** the boundaries) of any
other exploded bombs.

Yuki wants to know the **minimum** time needed to make all the bombs
exploded, and could you give her the answer?