Description
Description
A closed polygon is a figure bounded by a finite number of line segments. The intersections of the bounding line segments are called the vertices of the polygon. When one starts at any vertex of a closed polygon and traverses each bounding line segment exactly once, one comes back to the starting vertex.
A closed polygon is called convex if the line segment joining any two points of the polygon lies in the polygon. Figure 1 shows a closed polygon which is convex and one which is not convex. (Informally, a closed polygon is convex if its border doesn't have any "dents".)
The subject of this problem is a closed convex polygon in the coordinate plane, one of whose vertices is the origin (x = 0, y = 0). Figure 2 shows an example. Such a polygon will have two properties significant for this problem.
The first property is that the vertices of the polygon will be confined to three or fewer of the four quadrants of the coordinate plane. In the example shown in Figure 2, none of the vertices are in the second quadrant (where x < 0, y > 0).
To describe the second property, suppose you "take a trip" around the polygon: start at (0, 0), visit all other vertices exactly once, and arrive at (0, 0). As you visit each vertex (other than (0, 0)), draw the diagonal that connects the current vertex with (0, 0), and calculate the slope of this diagonal. Then, within each quadrant, the slopes of these diagonals will form a decreasing or increasing sequence of numbers, i.e., they will be sorted. Figure 3 illustrates this point.
Input
The input lists the vertices of a closed convex polygon in the plane. The number of lines in the input will be at least three but no more than 50. Each line contains the x and y coordinates of one vertex. Each x and y coordinate is an integer in the range -999..999. The vertex on the first line of the input file will be the origin, i.e., x = 0 and y = 0. Otherwise, the vertices may be in a scrambled order. Except for the origin, no vertex will be on the x-axis or the y-axis. No three vertices are colinear.
Output
The output lists the vertices of the given polygon, one vertex per line. Each vertex from the input appears exactly once in the output. The origin (0,0) is the vertex on the first line of the output. The order of vertices in the output will determine a trip taken along the polygon's border, in the counterclockwise direction. The output format for each vertex is (x,y) as shown below.
Sample Input
0 0
70 -50
60 30
-30 -50
80 20
50 -60
90 -20
-30 -40
-10 -60
90 10
Sample Output
(0,0)
(-30,-40)
(-30,-50)
(-10,-60)
(50,-60)
(70,-50)
(90,-20)
(90,10)
(80,20)
(60,30)
In the Blackjack card game, the player and the dealer are dealt two cards initially. One of dealer's cards is dealt face up and is known to the player but the other one is dealt face down. Given the two initial cards you are dealt and the dealer's face-up card, you are asked to compute the probability that your two-card hand is better than the dealer's two-card hand. This is not simple: the probability changes as the game is played because cards are dealt from the decks without replacement. To simplify the problem, we will only compute the probability when the cards are first dealt from the decks. That is, no cards have been dealt from the decks before.
In this game, an Ace has a value of 1 or 11 (chosen by the person holding the cards), the face cards (K, Q, J) have a value of 10, and the values of the remaining cards are given by their numerical values. The player wins against the dealer if:
the total value of the player's hand does not exceed 21; and
the total value of his hand is higher than that of the dealer or the total value of the dealer's hand exceeds 21.
The value of an Ace is chosen to maximize the total value without exceeding 21. If we are only interested in two-card hands, it is impossible for the total value to exceed 21.
Skilled players remember which cards have already been dealt and make decisions accordingly. To make this difficult, many casinos use multiple decks of cards to play the game. Each deck has 52 cards, 4 of each of A, K, Q, J, T (10), 9, ..., and 2.
Input
The input consists of a number of test cases. Each test case starts with a line containing a positive integer n (n <= 10) indicating the number of decks used. This is followed by a line containing 3 characters (separated by a space) in the set {A, K, Q, J, T, 9, ..., 2}, representing the dealer's face-up card and your two cards in the hand. In each case, assume that the n decks have been shuffled together randomly. The end of input is specified by n = 0.
Output
For each hand dealt, print on a line the probability of winning as a percentage, rounded to 3 decimal places. Separate the output of each case by a blank line.
Sample Input
1
T A J
4
2 3 4
0
Sample Output
93.878%
21.951%
