There are several airports in one country, and there are flights between some of them. One can fly from any airport to any other, probably with some changes. For any pair of airports there exists only one sequence of flights that connects them.

Two terrorists play a game. They make moves in turn. Each move consists of the following operations. A player mines an airport, chooses a flight and flies away together with his colleague. After the take-off he actuates a radio–controlled fuse. As a result the airport that the terrorists have just left is destroyed, and all the flights to and from this airport are no longer possible. After the aircraft lands the other player makes his move, and so forth. One loses if one cannot make a move.

Given an initial list of flights and the number of an airport where the terrorists are at the start of the game, write a program which would determine who wins if the terrorists play a perfect game (each chooses the best move).

The first line of an input file contains two integers: N and K separated with a space. Here N is the number of airports (N <= 1000) and K is the number of an airport, which is the starting point of the game (1 <= K<= N). The next n–1 lines of the file contain pairs of integers separated with a space. These integers are numbers of airports, connected with a flight (all the flights are symmetric and are mentioned only once). There are at most 20 flights to each airport. Input data are always correct.

There is a polygon A₁A₂…A_n (the vertices A_i are numbered in the clockwise order). On each side A_iA_i+1 an isosceles triangle A_iM_iA_i+1 is built on the outer side of the polygon, and angle A_iM_iA_i+1 = a_i. Here A_n+1 = A₁.

The set of angles a_i satisfies a condition that the sum of angles in any of its nonempty subsets is not aliquot to 360 degrees.

You are given n <= 50, co-ordinates of vertices M_i and angles a _i (measured in degrees). Write a program which restores co-ordinates of the polygon vertices.

The first line of an input file contains an integer n. The next n lines contain pairs of real numbers which are co-ordinates of points M_i. And the last n lines of the file consist of degree values of angles a_i.

The output file should contain n lines of pairs of coordinates of the points A_i.

There is a sequence of n+2 elements a₀, a₁,…, a_n+1 (n <= 3000, -1000 <= a_i <=1000). It is known that a_i = (a_i–1 + a_i+1)/2 – c_i for each i=1, 2, ..., n.

You are given a₀, a_n+1, c₁, ... , c_n. Write a program which calculates a₁.

The first line of an input file contains an integer n. The next two lines consist of numbers a₀ and a_n+1 each having two digits after decimal point, and the next n lines contain numbers c_i (also with two digits after decimal point), one number per line.

The output file should contain a₁ in the same format as a₀ and a_n+1.

The creators of a new programming language D++ have found out that whatever limit for SuperLongInt type they make, sometimes programmers need to operate even larger numbers. A limit of 1000 digits is so small... You have to find the sum of two numbers with maximal size of 1.000.000 digits.

The first line of an input file contains a single number N (1<=N<=1000000) — the length of the integers (in order to make their lengths equal, some leading zeroes can be added). It is followed by these integers written in columns. That is, the next N lines contain two digits each, divided by a space. Each of the two given integers is not less than 1, and the length of their sum does not exceed N. Output file should contain exactly N digits in a single line representing the sum of these two integers.

Ten mathematicians are flying on a balloon over the Pacific ocean. When they are crossing the equator they decide to celebrate this event and open a bottle of champagne. Unfortunately, the cork makes a hole in the balloon. Hydrogen is leaking out and the balloon is descending now. Soon it will fall into the ocean and all the balloonists will be eaten by hungry sharks.

But not everything is lost yet. One of the balloonists can sacrifice himself jumping out, so that his friends would live a little longer. Only one problem still exists ¾ who is the one to get out. There is a fair way to solve this problem. First, each of them writes an integer a_i not less than 1 and not more than 10000. Then they calculate the magic number N that is the number of positive integer divisors of the product a₁·a₂·…·a₁₀. For example, the number of positive integer divisors of 6 is 4 (they are 1,2,3,6). The hero (a mathematician who will be thrown out) is determined according to the last digit of N. Your task is to find this digit.

Input file contains ten numbers separated by a space. Output file should consist of a single digit from 0 to 9 — the last digit of N.

Input will consist of several lines of text containing a number of double quotes ("), as well as some TeX commands. End of file will be marked by an \endinput command.

Output will be an exact replica of the input, except the double quotes are to be modified according to the rules described above.

Sample Input

There is no "q in this sentence. \par

"Talk child," said the unicorn.

She s\"aid, "\thinspace ‘Enough!', he said."

\endinput

There is no q in this sentence. \par

‘‘Talk child,’’ said the unicorn.

She s\"aid, ‘‘\thinspace ‘Enough!', he said.''

\endinput

There is an infinite grid and an m´ n rectangle of stones on it (1 <= m,n <= 1000). The stones are located in the knots of the grid.

A following game for a single player is being played. One stone can jump over another along a vertical or a horizontal line. A stone which had been overjumped is taken away. The purpose of the game is to minimize number of stones on a grid.

Given a pair of numbers m and n separated with one space in an input file you are to write a program which should determine a minimal number of the stones left on the grid.

A good hunter kills two rabbits with one shot. Of course, it can be easily done since for any two points we can always draw a line containing the both. But killing three or more rabbits in one shot is much more difficult task. To be the best hunter in the world one should be able to kill the maximal possible number of rabbits. Assume that rabbit is a point on the plane with integer x and y coordinates. Having a set of rabbits you are to find the largest number K of rabbits that can be killed with single shot, i.e. maximum number of points lying exactly on the same line. No two rabbits sit at one point.

An input file contains an integer N (2<=N<=200) specifying the number of rabbits. Each of the next N lines in the file contains the x coordinate and the y coordinate (in this order) separated by a space (-1000<=x,y<=1000).

The output file contains the maximal number K of rabbits situated in one line.