B. Pizza After the Contest
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

After five hours of intense competition, the participants deserved some rest and pizza! The organizers only need to determine how many pizzas to order so that nobody is left out.

There were $$$N$$$ teams in the contest, and each team had exactly three people, so there were $$$3N$$$ participants in total. The pizzeria offers pizzas of two sizes:

  • diameter $$$30$$$ centimeters, cut into $$$6$$$ equal slices;
  • diameter $$$40$$$ centimeters, cut into $$$8$$$ equal slices.
All pizzas are round and have the same thickness, so the amount of pizza received by a participant is determined by the total area of the slices given to them.

Each participant must receive at least one slice. At the same time, all participants must receive the same amount of pizza by area. One participant may be given slices from different pizzas, including pizzas of different sizes. Slices cannot be cut further. Some slices may be left undistributed.

The organizers want to order the minimum total number of pizzas. Among all ways to order and distribute pizzas with that number of pizzas, they choose the one with the minimum total area of undistributed slices.

Determine how many pizzas of each size should be ordered.

Input

The only line contains one integer $$$N$$$ $$$(1 \le N \le 10^9)$$$ — the number of teams. Each team has exactly three people, so there are $$$3N$$$ participants in total.

Output

Print two non-negative integers separated by a space — the number of pizzas with diameter $$$30$$$ centimeters and the number of pizzas with diameter $$$40$$$ centimeters in the optimal order.

An answer always exists. If there are several optimal answers (with the minimum total number of pizzas and the minimum total area of undistributed slices), print any of them.

Note that the number of ordered pizzas should be minimized first. The total area of undistributed slices is minimized among the options with the same number of ordered pizzas.

Examples
Input
1
Output
1 0
Input
3
Output
2 0
Input
5
Output
0 2
Note

Let the area of one slice of a $$$30$$$ cm pizza be $$$37.5\pi$$$ (the area of a circle of radius $$$15$$$, divided by $$$6$$$), and the area of one slice of a $$$40$$$ cm pizza be $$$50\pi$$$ (the area of a circle of radius $$$20$$$, divided by $$$8$$$).

Example 1. For $$$N = 1$$$, there are $$$3$$$ people. If one $$$30$$$ cm pizza is ordered, it is cut into $$$6$$$ slices, and each of the $$$3$$$ participants can be given $$$2$$$ slices — all participants receive the same area $$$2 \cdot 37.5\pi = 75\pi$$$, and all $$$6$$$ slices are distributed without leftovers. Fewer than one pizza cannot be ordered, so this is the optimal order. Answer: 1 0.

Example 2. For $$$N = 3$$$, there are $$$9$$$ people. Consider an order of two pizzas:

  • two $$$30$$$ cm pizzas give $$$12$$$ slices; each of the $$$9$$$ participants can be given $$$1$$$ slice of area $$$37.5\pi$$$, and $$$3$$$ slices will remain undistributed — the total area of the remainder is $$$3 \cdot 37.5\pi = 112.5\pi$$$;
  • two $$$40$$$ cm pizzas give $$$16$$$ slices; each of the $$$9$$$ participants can be given $$$1$$$ slice of area $$$50\pi$$$, and $$$7$$$ slices will remain undistributed — the total area of the remainder is $$$7 \cdot 50\pi = 350\pi$$$.
It is impossible to order fewer than two pizzas: one pizza of either size gives at most $$$8$$$ slices, but at least $$$9$$$ slices are needed (one per participant), so the minimum total number of pizzas is two. Among orders of two pizzas, the option with two $$$30$$$ cm pizzas gives a smaller area of undistributed slices ($$$112.5\pi \lt 350\pi$$$), so it is optimal. Answer: 2 0.

Example 3. For $$$N = 5$$$, there are $$$15$$$ people. By ordering two $$$40$$$ cm pizzas, we get $$$16$$$ slices; each of the $$$15$$$ participants receives $$$1$$$ slice of area $$$50\pi$$$, and $$$1$$$ slice remains undistributed. It can be checked that among all orders with the minimum total number of pizzas, this option gives the smallest remainder area. Answer: 0 2.