# Coins

Xorin, the main character from The Wolf of XOR Street, is now the youngest billionaire-in-coins ever. His wife, Xoranna, wants to steal his money. They are going to play the game Xorin is addicted to. Because Xoranna is a beautiful young blonde girl, she always starts. Your task is to help Xoranna steal the money from Xorin by winning the game. If you manage to do so, Xoranna is going to give you a quarter of the fortune.

The rules of the game are the following:

• The game is played in turns and Xoranna always starts the game.
• The game is played on a fixed size circular table of radius SZ.
• Every player has to put a radius 1 coin on the table without overlapping existing coins (they can, however, be tangent).

# Interaction

The turns alternate and you will have to place a coin in the first turn (print the x and the y coordinate of the coin).

The AI will put his coin after your turn (printing two values: x and y). It is guaranteed that the AI puts the coin in a valid position.

Note: After each command you should print a newline character and flush the output (using functions such as `fflush(stdout)` or `cout.flush()`).

The interactions stops when the AI can't make any valid move.

# Constraints

• 5 ≤ SZ ≤ 20
• Every point of each coin must be on the table.
• Point (0, 0) is the center of the cicular board.
• We test the correctness of the placement of the coins with a 10-6 precision.

# Helper functions

```    1 pair<double,double> rot(double x,double y,double x2,double y2,double U)
2 {
3     x -= x2;
4     y -= y2;
5     double new_x = x * cos(U) - y * sin(U);
6     double new_y = x * sin(U) + y * cos(U);
7    new_x += x2;
8    new_y += y2;
9    return make_pair(new_x,new_y);
10 }
11
12 pair<double,double> sim(double x,double y,double x2,double y2)
13 {
14     return make_pair(x2-x,y2-y);
15 }
```

# Example interaction

User programSimulator
10
1 2
-9 0
3 2
-8 -4
10 5
Questions?