A pirate's treasure map typically contains a series of instructions which, if followed, lead you from the landing place on a desert isle to the spot marked X where the treasure is buried. You are to construct such a series of instructions for a particular desert isle.

The island is a circle with radius r paces whose centre is at (0,0). Relative to the centre, the point (0,1) is north, (0,-1) is south, (1,0) is east, and (-1,0) is west. Also, (1,1) is northeast, (1,-1) is southeast, (-1,1) is northwest, and (-1,-1) is southwest.

The landing place, on the circumference, is specified by its coordinates. The spot marked X, on the surface of the island is also specified by its coordinates.

Each instruction in the sequence should have the form

   direction distance

where

is one of { north, south, east, west, northeast, northwest, southeast, southwest } and

is a non-negative real number indicating the number of paces to be travelled in the given direction. When executed as a sequence the instructions should lead from the landing place to the spot marked X without leaving the island. The total distance (that is, the sum of the distances in your sequence) should be minimized. From the possible sequences that minimize total distance, choose one with the minimum number of instructions.

Input will consist of a number of test cases, followed by a line containing -1. Each test case consists of a single line containing five real numbers: r, x, y, X, Y. r is the radius of the island; x,y are the coordinates of the landing place; X,Y are the coordinates of the spot marked X. The landing place and the spot marked X are distinct.

For each test case, output the sequence, one instruction per line. Distances should be accurate to ten places after the decimal, as shown. Output an empty line between test cases.

The first line of input contains one integer giving the number of cases that follow. The data for each case start with two integer numbers: the length of the pole (in cm) and n, the number of ants residing on the pole. These two numbers are followed by n integers giving the position of each ant on the pole as the distance measured from the left end of the pole, in no particular order. All input integers are not bigger than 1000000 and they are separated by whitespace.

For each case of input, output two numbers separated by a single space. The first number is the earliest possible time when all ants fall off the pole (if the directions of their walks are chosen appropriately) and the second number is the latest possible such time.

In strong winds, sailboats tend to heel leeward (tilt away from the wind) like the one in the picture. Heeling is undesirable for at least two reasons. First, the effective sail area is reduced, as the effective height of the sail is multiplied by the cosine of the angle. Reduced sail area implies reduced speed. Second, the boat may heel to the point that its centre of gravity ceases to be above the hull, causing the boat to capsize.

To mitigate these problems, catamarans like the one shown split the hull into two pieces (the port and starboard hulls). This design increases the effective width of the boat. Increased width decreases the vertical mechanical advantage of the sail, thus reducing heeling. Increased width also increases the angle of heeling that can be tolerated before the boat capsizes.

Heeling can also be mitigated by having the crew sit or stand on, or even hike out beyond, the windward hull. If you look carefully at the picture you can see the two person crew hiking to windward.

At some wind velocity, even these measures are insufficient to keep the boat upright. A skipper's only choice (other than to capsize) is to let out the sail, which reduces its effective horizontal dimension much as heeling reduces its vertical dimension. As with heeling, this action causes loss of speed. If the boat heels sufficiently, it may not even be possible to let out the sail, as its outer corner may be obstructed by the surface of the water!

Reefing is a mechanism for reducing the sail's area. Roller reefing involves wrapping the sail around the boom (much like a window blind) so as to reduce its height. With sufficient reefing, the heeling can be controlled in almost any wind.

But reefing involves reduced speed, so our skipper has elected yet another approach. She has decided to beach the boat and pick up some rocks to use as ballast. Ballast is just dead weight added to hull, which tends to counteract heeling. It slows the boat a bit (as it rides lower in the water) but not nearly so much as reducing sail area.

Given n rocks, you are to compute how to divide them between the port and starboard hulls so that the weight of rocks in each hull is nearly equal.

Input contains several test cases. Each test case begins with 1 < n ≤ 100; the number of rocks to be added as ballast. Consider the rocks to be numbered 1 through n. n lines follow; the ith line gives the weight in kg of the ith rock - a positive real number not greater than 100. A line containing 0 follows the last test case.

For each test case, output a single line giving the numbers of the rocks that should be loaded as ballast into the starboard hull. Assume that the other rocks will be loaded into the port hull. The total weight of ballast in the port hull should not differ from that in the starboard hull by more than 2%. If there are many solutions, any one will do. There will always be a solution; indeed, there will always be a solution that balances within 1%, but you aren't required to find it.

]]> Please Input Input Here

• swap "ad" to yield "mamda"
• swap "md" to yield "madma"
• swap "ma" to yield "madam"

The first line of input gives n, the number of test cases. For each test case, one line of input follows, containing a string of up to 100 lowercase letters. Output consists of one line per test case. This line will contain the number of swaps, or "Impossible" if it is not possible to transform the input to a palindrome.

Many coins are available for these tables, including foreign and special commemorative coins. Given an inventory of available coins and a desired table height, compute the lengths nearest to the desired height for which four legs of equal length may be constructed using a different coin for each leg.

Input consists of several test cases. Each case begins with two integers: 4 ≤ n ≤ 50 giving the number of types of coins available, and 1 ≤ t ≤ 10 giving the number of tables to be designed. n lines follow; each gives the thickness of a coin in hundredths of millimetres. t lines follow; each gives the height of a table to be designed (also in hundredths of millimetres). A line containing 0 0 follows the last test case.

For each table, output a line with two integers: the greatest leg length not exceeding the desired length, and the smallest leg length not less than the desired length.