Problem Statement

There are $N$ kinds of items, each with infinitely many copies. The $i$-th kind of item has a weight of $A_i$, a volume of $B_i$, and a value of $C_i$.

Level $X$ Takahashi can carry items whose total weight is at most $X$ and whose total volume is at most $X$. Under this condition, it is allowed to carry any number of items of the same kind, or omit some kinds of items.

Let $f(X)$ be the maximum total value of items Level $X$ Takahashi can carry. It can be proved that the limit $\displaystyle\lim_{X\to \infty} \frac{f(X)}{X}$ exists. Find this limit.

Constraints

• $1\leq N\leq 2\times 10^5$
• $10^8\leq A_i,B_i,C_i \leq 10^9$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

N
A_1 B_1 C_1
A_2 B_2 C_2
\vdots
A_N B_N C_N

Output

Print the answer. Your output will be considered correct if the absolute or relative error from the judge's answer is at most $10^{-6}$.