Let's fly!

Malysh and Karlson decided to go out for a walk. More precisely, a flight. Karlson, being a responsible person, drew up a flight plan and showed it to Malysh. The plan works like this: for every moment in time $i$, Karlson assigned an altitude $h_i$ at which he will be flying at that moment.

But after yet another round of eating too much jam, Malysh did not like the altitude changes in Karlson's plan. He decided to adjust the plan slightly so that the flight stays at one altitude the whole time. Karlson, in turn, said he would be very upset if Malysh changed the plan a lot. Precisely: if Malysh changes the altitude at moment $i$ by one meter, Karlson's displeasure grows by $a_i$, where $a_i$ is how much Karlson wants to fly at altitude $h_i$ at moment $i$.

So Malysh can change the altitude at any point by any amount, but replacing $h_i$ with $h_i \pm c_i$ at point $i$ increases Karlson's displeasure by $c_i \cdot a_i$. Help Malysh fix the plan by replacing all altitudes with one single value, so that Karlson's displeasure is minimal.

The first line contains one integer $n$ ($1 \le n \le 10^5$), the duration of the flight. The second line contains $n$ integers $h_i$ ($1 \le h_i \le 10^6$), the altitude at moment $i$. The third line contains $n$ integers $a_i$ ($1 \le a_i \le 10^6$), Karlson's displeasure coefficient at moment $i$.

Print two numbers: the final altitude of the flight and the total displeasure of Karlson. If several altitudes are possible, print the smallest one.

If there are several answers, print the lexicographically smallest pair.