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H. Stock Exchange

time limit per test

6 secondsmemory limit per test

16 megabytesinput

standard inputoutput

standard outputWarning: This problem has an unusual memory limit!

Bob decided that he will not waste his prime years implementing GUI forms for a large corporation and instead will earn his supper on the Stock Exchange Reykjavik. The Stock Exchange Reykjavik is the only actual stock exchange in the world. The only type of transaction is to take a single share of stock $$$x$$$ and exchange it for a single share of stock $$$y$$$, provided that the current price of share $$$x$$$ is at least the current price of share $$$y$$$.

There are $$$2n$$$ stocks listed on the SER that are of interest to Bob, numbered from $$$1$$$ to $$$2n$$$. Bob owns a single share of stocks $$$1$$$ through $$$n$$$ and would like to own a single share of each of $$$n+1$$$ through $$$2n$$$ some time in the future.

Bob managed to forecast the price of each stock — in time $$$t \geq 0$$$, the stock $$$i$$$ will cost $$$a_i \cdot \lfloor t \rfloor + b_i$$$. The time is currently $$$t = 0$$$. Help Bob find the earliest moment in time in which he can own a single share of each of $$$n+1$$$ through $$$2n$$$, and the minimum number of stock exchanges he has to perform in order to do that.

You may assume that the Stock Exchange has an unlimited amount of each stock at any point in time.

Input

The first line contains a single integer $$$n$$$ ($$$1 \leq n \leq 2200$$$) — the number stocks currently owned by Bob.

Each of the next $$$2n$$$ lines contains integers $$$a_i$$$ and $$$b_i$$$ ($$$0 \leq a_i, b_i \leq 10^9$$$), representing the stock price of stock $$$i$$$.

Output

If it is impossible for Bob to achieve his goal, output a single integer $$$-1$$$.

Otherwise, output two integers $$$T$$$ and $$$E$$$, where $$$T$$$ is the minimum time in which he can achieve his goal, and $$$E$$$ is the minimum number of exchanges in which he can achieve his goal at time $$$T$$$.

Examples

Input

1 3 10 1 16

Output

3 1

Input

2 3 0 2 1 1 10 1 11

Output

6 3

Input

1 42 42 47 47

Output

-1

Input

8 145 1729363 891 4194243 424 853731 869 1883440 843 556108 760 1538373 270 762781 986 2589382 610 99315884 591 95147193 687 99248788 65 95114537 481 99071279 293 98888998 83 99764577 769 96951171

Output

434847 11

Input

8 261 261639 92 123277 271 131614 320 154417 97 258799 246 17926 117 222490 110 39356 85 62864876 86 62781907 165 62761166 252 62828168 258 62794649 125 62817698 182 62651225 16 62856001

Output

1010327 11

Note

In the first example, Bob simply waits until time $$$t = 3$$$, when both stocks cost exactly the same amount.

In the second example, the optimum strategy is to exchange stock $$$2$$$ for stock $$$1$$$ at time $$$t = 1$$$, then exchange one share of stock $$$1$$$ for stock $$$3$$$ at time $$$t = 5$$$ (where both cost $$$15$$$) and then at time $$$t = 6$$$ exchange the second on for the stock number $$$4$$$ (when they cost $$$18$$$ and $$$17$$$, respectively). Note that he can achieve his goal also with only two exchanges, but this would take total time of $$$t = 9$$$, when he would finally be able to exchange the share number $$$2$$$ for the share number $$$3$$$.

In the third example, Bob can never achieve his goal, as the second stock is always strictly more expensive than the first one.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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