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1492. Vasya's Dad 2

Time limit: 1.0 second
Memory limit: 64 MB
Vasya is a young mathematician. Sometimes it happens that Vasya's homework includes many complicated mathematical problems, but Vasya is not upset about it. Why is it so? The fact is that Vasya's father is good at mathematics.
In one of the problems Vasya asked his father to solve, the notion of a piecewise linear function is introduced. A piecewise linear function is a function y = f(x) whose graph in the coordinate system (xy) is a broken line with vertices (x1y1), (x2y2), …, (xNyN). The following conditions must hold: no three successive vertices belong to the same line; xi > xi−1 for i > 1; and x1 = −xN. In Vasya's textbook, vertices of this broken line are called breakpoints of the function. A piecewise linear function is called even if for each x from [x1xN] it holds f(−x) = f(x), and a function is called odd if for each x from [x1xN] it holds f(−x) = −f(x).
Vasya's task is to determine for a given piecewise linear function if it can be represented as a sum of an even piecewise linear function and odd piecewise linear function.

Input

The first line contains an integer N (2 ≤ N ≤ 30000). The next N lines contain the coordinates of the breakpoints of a piecewise linear function (xiyi). These are integers in the range from −15000 to 15000.

Output

Output "Yes" if the given function can be represented as a sum of an even piecewise linear function and an odd piecewise linear function. Then output the coordinates of the breakpoints of the even function, and after that output the coordinates of the breakpoints of the odd function. The coordinates of each breakpoint must be given in a separate line. Each coordinate must contain at least four fractional digits. If the given function cannot be represented in such a form, then output "No".

Sample

inputoutput
2              
-1 0
1 0
Yes
-1.0000 0.0000
1.0000 0.0000
-1.0000 0.0000
1.0000 0.0000
Problem Author: Fedor Fominykh
Problem Source: XIII-th USU Junior Contest, October 2006