C. Tomorrow Will Be Better Than Yesterday
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Pavel knows for sure — tomorrow is always better than yesterday.

He decided to prove this using geometry.

To do this, Pavel considered n consecutive days and assigned a point on the plane (xi, yi) to each day.

He considers day i + 1 to be better than day i if one of the two conditions is met:

  • either xi < xi + 1;
  • or xi = xi + 1, but yi < yi + 1.

Pavel is only unsure about one thing — whether he has chosen the correct coordinate system for his calculations. He is confident that only rotations and/or reflections can be used to find the correct coordinate system.

Help Pavel — find any rectangular (orthogonal) coordinate system in which each subsequent day will be better than the previous one.

Input

The first line contains an integer n (1 ≤ n ≤ 105) — the number of days analyzed by Pavel.

Each of the following n lines contains two integers xi and yi ( - 105 ≤ xi,  yi ≤ 105) — the point assigned by Pavel to the i-th day.

Output

In the first line, print YES if such a rectangular coordinate system exists, and NO otherwise.

If the desired coordinate system exists, print two more lines.

In the second line, print two integers Xx and Yx (|Xx|, |Yx| ≤ 109;|Xx| + |Yx| > 0) — the coordinates of the vector aligned with the axis Ox of the new coordinate system.

In the third line, print two integers Xy and Yy (|Xy|, |Yy| ≤ 109;|Xy| + |Yy| > 0) — the coordinates of the vector aligned with the axis Oy of the new coordinate system.

The vectors (Xx, Yx) and (Xy, Yy) must be perpendicular to each other.

If there are multiple valid answers, print any.

Examples
Input
9
3 3
2 3
3 2
1 3
2 2
3 1
1 2
2 1
1 1
Output
YES
-1 -1
1 -1
Input
4
1 1
1 2
2 2
2 1
Output
NO
Input
1
100000 100000
Output
YES
-100000 100000
-100000 -100000
Input
2
0 0
0 0
Output
NO
Note

First test example

First, consider the points assigned to the days and the found vectors in the original coordinate system:

Now let's show these same points in the coordinate system based on the found vectors:

The coordinates of the points after transitioning to the new coordinate system:

  1. (3, 3) — ( - 3, 0);
  2. (2, 3) — ( - 2.5,  - 0.5);
  3. (3, 2) — ( - 2.5, 0.5);
  4. (1, 3) — ( - 2,  - 1);
  5. (2, 2) — ( - 2, 0);
  6. (3, 1) — ( - 2, 1);
  7. (1, 2) — ( - 1.5,  - 0.5);
  8. (2, 1) — ( - 1.5, 0.5);
  9. (1, 1) — ( - 1, 0).

It is clear that each subsequent point is "better" than the previous one in the new coordinate system.