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?