Ttangttangba Split

Do you know how two people can split a Ssangssangba (쌍쌍바) fairly? The method goes like this.

• A splits the Ssangssangba.
• B picks one of the pieces and eats it.
• A eats the remaining pieces that B did not pick.

Junseong and Seongu find a treasure map at the same time. It shows a coordinate plane and $N$ treasures, where treasure $i$ has value $v_i$. They modify the method above to split the treasures fairly.

• Junseong draws the line $ax = by$ on the coordinate plane. ($0 < \max(|a|, |b|) \le 2 \times 10^9$)
• Seongu picks one of the two resulting planes and takes all treasures on that plane. Treasures on the line also go to Seongu.
• Junseong takes all treasures that Seongu does not take.

Seongu always picks the plane whose treasure value sum is not smaller than the other plane's. Help the poor college student Junseong draw the line so that the sum of values Junseong takes is maximized.

The first line contains an integer $N$. ($1 \le N \le 111\,222$)

Each of the next $N$ lines contains $x_i$, $y_i$, $v_i$, meaning treasure $i$ is at coordinate $(x_i, y_i)$ and has value $v_i$. The values of $-10^9 \le x_i, y_i \le 10^9$ and $1 \le v_i \le 10^9$ hold. All of $x_i$, $y_i$, and $v_i$ are integers.

Print two integers $a$ and $b$ separated by a space, so that the sum of values Junseong takes is maximized. If several answers exist, print any of them.